I don't know exactly why but like many other languages, it's all about etymology (roots/origin(s) of the word) and usage. And as you said yourself nouns ending with -a are usually feminine. Keyword: usually. In other words, not all nouns ending with -a are feminine and not all feminine nouns end with -a.

masculine: un/el clima, problema, día

feminine: una/la canción, universidad, nube

Maybe there was a slight detail you got wrong.

So unfair!!

Agian so unfair

If the modifier is a noun, the article "de" is used..

a physics class - una clase de física

But if it's an adjective, the article is not used..

an important class - una clase importante

Clase I believe is a feminine noun, so it take una as a modifier instead of un

no because "clase" is a feminine noun

Nouns go before adjectives and clase is a feminine noun so you use 'una' instead of the masculine 'un'.

It isn't a game lol

its not a game so shut up

This isn't a game, buddy.... It's a learning tool, and if you don't want to use it, then don't.