Why must I add "-a" after "десерт"? Is it a casing thing I've overlooked?
You must use Genitive case with the word нет.
I learned that dessert was сладкое some twenty years ago. Is this a normal translation?
Сладкое, though still understood, is an antiquated word. Десерт is the standard today.
It would mean "something sweet", dessert is usually after dinner (обед), something sweet can be a snack at any time.
У меня нет ничего сладкого. -- You can say the phrase this way.
Are there many words like "net" that require you to put a the genative ending