Why student is written with an ą ?
Because the case you have to use in this sentence is not the nominative. "Moja córka to studentka", but "Moja córka jest studentką", see https://en.wiktionary.org/wiki/studentka#Polish.
Why can't we say "My daughter is student" instead of "a student"
English is very consistent about putting an article in front of nouns, so writing "My daughter is a student" follows standard English rules and omitting the "a" is incorrect.
Can we have some link about this rule? Saying "He is student" doesn't sound bad to me. Thanks!
"In English, an indefinite article is needed in front of professions."
Zła intonacja lektora - jak w zdaniu pytającym!
Why is "Moja córka jest studentkou" not acceptable? (My daughter is a female student.) Clunky, but technically correct.
Studentkou? That belongs in the Czech course, I'm afraid. The feminine instrumental ending in Polish is -ą.