Thank you so much for your answer.
I need to ask you, is there a good video on what is the difference between falsetto and head voice? Cause I thought I understood it, but as I can see now I was wrong all along. I watched this video and though I got it, but if you are right, then you've confused me. And teacher told me as well that the "And I'll tell you all about it when I see you again" part is a falsetto.
About the vocal teacher, she never told me anything about these stuff. I don't even know how are these things called in my native language (Czech). We usually just warm up and they I sing a couple of songs. Sometimes she tells me it was good and then we go on, sometimes we correct some notes, runs that were not in pitch, a lot of times she tells me to sing lower songs, because my voice sounds good there, but I always disagree there. And yes, she does say that I should sing inside my comfort zone and when it will sound good, I should move higher and I do partly agree with her, cause I do think it is important to sound good even at around G3, but I should train the high notes as well.
All I have learned, I learned from watching youtube videos and picking, what seems to work for me. I don't really want to stick with one course as there are so many and sometimes, the teachers can be wrong. For example I saw Ken Tamplin (he is always in the recommended videos, don't really like him, but he did show me the lip roll warm up) and I saw the lizard tongue thing, which was just weird.
It really flatters me to hear my colour sounds like Paul McCartney but I have a long way to go But truly thank you, as almost everybody I didn't really like my voice on the recording.
I did hear about Robert Lunte and I am thinking about watching some videos or even buying some stuff. I did spare some money and I really want to train my voice to sing pop/rock with ease and beatiful tone. But I think that Robert sings a lot different than I would want to sing. He uses a lot of screams and distorted sounds and I am not really into that. I do like it sometimes (John Lennon, Oasis), but just subtle use of it.