kickingtone

I was really only mentioning another option, rather than an improvement on how you chose to sing. I think that your voice seems to also be suited to a smooth mezzo sound. Maybe that could be something to explore and try out on another song some time. See how that goes down. You could be pleasantly surprised.
YouTube has its fair share of trolls, a small minority to be ignored. People with bizarre complexes can go to weird lengths to try to discourage you. Don't give them undue attention. That would be my only YouTube advice.

(Nice background story.)
I'd say that practically all songs are challenging. If you are not challenged, you either don't get the song, or you are not working hard enough.
Anyway, to give a credible performance the way you did, and to do it a cappella (nowhere to hide), would definitely challenge a lot of singers.
I'm hearing more heady tones, and less of the "darker mezzo" sound. I can hear the darker rich mezzo tones "lurking" in your voice, but you don't really bring them out?
Maybe I am biased. All my favourite female singers use that mezzo sound.
(You in London? Brexit just took a nasty turn with the permanent status application thing.)

(Nice background story.)
I'd say that practically all songs are challenging. If you are not challenged, you either don't get the song, or you are not working hard enough.
Anyway, to give a credible performance the way you did, and to do it a cappella (nowhere to hide), would definitely challenge a lot of singers.
I'm hearing more heady tones, and less of the "darker mezzo" sound. I can hear the darker rich mezzo tones "lurking" in your voice, but you don't really bring them out?
Maybe I am biased. All my favourite female singers use that mezzo sound.
(You in London? Brexit just took a nasty turn with the permanent status application thing.)

[Constriction and "choking" can also be a protective reflex. If the body detects that the pressure or airflow at the throat is unhealthy, it says, "forget the singing" and reflexes to shut off the problem. Just like your "blink" reflex, it is not a good idea to try to simply override it psychologically. You need to address the thing that is causing the reflex. For singing this is likely to be something like inadequate breath support.]
Anyway, back to the OP. Decent vocals, imo.
With proper diaphragmatic breath support, your voice will glide effortlessly straight over the passaggio, and you will get that responsiveness and agility you are looking for. I notice in classical training techniques that they make a big deal out of breath support (probably coming from traditions of singing without a mic), and relatively less of a deal about the passaggio (even though the term comes out of that pedagogy). Once you are able to employ a good diaphragmatic breath support method, .like appoggio, the passaggio is no longer a big challenge. It gets "fixed" almost automatically.
Add that to the fact that you are able to siren up to G5 (wobbly, but an impressive foundation), I think you can really take your vocals places. 
Yup, I am not a coach. Just my personal take. 

[Constriction and "choking" can also be a protective reflex. If the body detects that the pressure or airflow at the throat is unhealthy, it says, "forget the singing" and reflexes to shut off the problem. Just like your "blink" reflex, it is not a good idea to try to simply override it psychologically. You need to address the thing that is causing the reflex. For singing this is likely to be something like inadequate breath support.]
Anyway, back to the OP. Decent vocals, imo.
With proper diaphragmatic breath support, your voice will glide effortlessly straight over the passaggio, and you will get that responsiveness and agility you are looking for. I notice in classical training techniques that they make a big deal out of breath support (probably coming from traditions of singing without a mic), and relatively less of a deal about the passaggio (even though the term comes out of that pedagogy). Once you are able to employ a good diaphragmatic breath support method, .like appoggio, the passaggio is no longer a big challenge. It gets "fixed" almost automatically.
Add that to the fact that you are able to siren up to G5 (wobbly, but an impressive foundation), I think you can really take your vocals places. 
Yup, I am not a coach. Just my personal take. 

Part of gaining confidence is discovering that things are nowhere near as bad as you imagine.
It's a classic catch. You need the confidence to take the first step, but you need to take the first step to see what it is about and gain the confidence.
The other thing is that negative opinions and thoughts are only as potent as the attention you give them.
So forget all the imagined "horror" scenarios and think of the time when you are looking back and saying, "what on Earth was I worried about?". That is the prize you are aiming for.
As a start, bear in mind that any competent teacher has seen and heard it all before: singers of all abilities. All the teacher is thinking about is building a voice -- none of the negative opinions you may have grown up around. So it really is up to you to drop that fear. The teacher is not going to even bat an eyelid.
Listening to your clips, I would think that the first thing a teacher would tell you to do is to RELAX! Don't try to compensate for doubts in your head!
Think six months ahead, man. I am not hearing anything in your clips that could stop you from sweeping away all your doubts within six months.
It's your career. Is it worth that patience?
 

It is amazing to me how Bollywood manages to churn out these beautiful tunes. What genre is it?
(Sometimes, not understanding the language is a blessing. I am often disappointed if I see the translated lyrics. They are usually very average. )
Anyway, listening to you singing, I would say that you have good pitch appreciation (you may be  thinking, "of course", but it is a big deal for some beginners).
You do have some problems with execution as the pitch ascends (or occasionally as it fluctuates quickly), even though you seem to be aiming for the right notes.
It sounds to me as if this is mainly to do with breath regulation and is made more difficult with a genre of music that uses a lot of melisma and arpeggios.
I would recommend finding an appropriate diaphragmatic breathing technique. However, as I have not come across any coach or trainer of Western music who has correctly characterized the unique sound of this genre of singing,  I can't really say which diaphragmatic breathing technique will work well. Somehow the Indian singers manage to get a lot of "cry" in the upper range, while keeping the lower range mellow. Some Western trainers confuse this with breathiness.
In your singing, I think that the mellow lower end is going to come naturally. Breath control will be required to find the resonance in the upper range.
That's my two cents worth of opinion. 

It is amazing to me how Bollywood manages to churn out these beautiful tunes. What genre is it?
(Sometimes, not understanding the language is a blessing. I am often disappointed if I see the translated lyrics. They are usually very average. )
Anyway, listening to you singing, I would say that you have good pitch appreciation (you may be  thinking, "of course", but it is a big deal for some beginners).
You do have some problems with execution as the pitch ascends (or occasionally as it fluctuates quickly), even though you seem to be aiming for the right notes.
It sounds to me as if this is mainly to do with breath regulation and is made more difficult with a genre of music that uses a lot of melisma and arpeggios.
I would recommend finding an appropriate diaphragmatic breathing technique. However, as I have not come across any coach or trainer of Western music who has correctly characterized the unique sound of this genre of singing,  I can't really say which diaphragmatic breathing technique will work well. Somehow the Indian singers manage to get a lot of "cry" in the upper range, while keeping the lower range mellow. Some Western trainers confuse this with breathiness.
In your singing, I think that the mellow lower end is going to come naturally. Breath control will be required to find the resonance in the upper range.
That's my two cents worth of opinion. 

It is amazing to me how Bollywood manages to churn out these beautiful tunes. What genre is it?
(Sometimes, not understanding the language is a blessing. I am often disappointed if I see the translated lyrics. They are usually very average. )
Anyway, listening to you singing, I would say that you have good pitch appreciation (you may be  thinking, "of course", but it is a big deal for some beginners).
You do have some problems with execution as the pitch ascends (or occasionally as it fluctuates quickly), even though you seem to be aiming for the right notes.
It sounds to me as if this is mainly to do with breath regulation and is made more difficult with a genre of music that uses a lot of melisma and arpeggios.
I would recommend finding an appropriate diaphragmatic breathing technique. However, as I have not come across any coach or trainer of Western music who has correctly characterized the unique sound of this genre of singing,  I can't really say which diaphragmatic breathing technique will work well. Somehow the Indian singers manage to get a lot of "cry" in the upper range, while keeping the lower range mellow. Some Western trainers confuse this with breathiness.
In your singing, I think that the mellow lower end is going to come naturally. Breath control will be required to find the resonance in the upper range.
That's my two cents worth of opinion. 

I hear voices in the background. It may only be my (vivid) imagination, but you sound to me as if you don't want to attract too much attention to yourself. You sound as if you are singing to yourself.
If you are singing somewhere where you are not yet comfortable, I advise that it is an absolute MUST to find somewhere where you can relax. If you don't, you could end up training all kinds of inhibition and nervousness or tension into your voice.

I hear voices in the background. It may only be my (vivid) imagination, but you sound to me as if you don't want to attract too much attention to yourself. You sound as if you are singing to yourself.
If you are singing somewhere where you are not yet comfortable, I advise that it is an absolute MUST to find somewhere where you can relax. If you don't, you could end up training all kinds of inhibition and nervousness or tension into your voice.

I think quack or twang is caused by the air flow "spitting" through the folds. The harmonics it produces still have to be guided to your resonance centres to be amplified, and the more relaxed you vocal tract, the more it can shape as a wave guide.
Yep. Finding where the resonance feedback is will help you tune your vocal tract to best guide the sound.
And these Eureka moments are the best! They really bring out the researcher in me. Your vocal instrument is like a whole laboratory that you carry around with you, with the keys at you fingertips....yes.. the keys...