Can't we say "Bocs" ?
You can, but that's very colloquial and doesn't express too much regret.
Why bocsi isnt accepted?
it's too colloquial. You can say it to your friend and it doesn't express a high degree of regret.
From watching a native Hungarian speaker on youtube teach a few lessons, she said you could just simple say ''kösz'', is this not totally allowed or?
Kösz and köszi are less formal than köszönöm
They are colloquial terms to express "thanks". We normally don't use them in a formal conversation. E.g. a student should never say that to a teacher otherwise he or she would show total disrespect.
Why not "Sajnos" in place of "Bocsanat"?
"sajnos" means unfortunately, it's not used to mean "i am sorry".
Valaki szokta egyáltalán így mondani hogy elnézést, köszönöm? Csak szerintem hangzik furán? És csak én jöttem magyarként magyart tanulni?
nyugi én is magyarként tanulok magyart XD amúgy szerintem is tök furán hangzik az hogy bocsánat köszönöm
When I gave: Elnezest kerek, koszonom! my answer was rejected. Why? is it over the top to say kerek as well or does it change the meaning?
"elnézést, köszönöm" should be accepted.
The other proposed answers are unnatural and illogical, that they hardly pose any challenge.
("Sajnálom, ide szépen!" and "Menj, köszi!")
That's not even the point of Basic 1. it's actually just like other basic 1 lessons in this regard