Learn Danish: Jeg har mange æbler.

The singular word for apple is et æble. Because it already ends in an -e, you only need to add an -r to make the plural æbler. You typically add -er to nouns that end in a consonant.

Does the gender of æble matter when making it plural?

Not for this type of plural! Whether a noun is an en word or an et word, if it follows the regular rule of adding -er or -r, the gender doesn't change the ending. Both et æble (an apple) and en pige (a girl) just take an -r in the plural: æbler and piger.

Could I use meget instead of mange to say "a lot of apples"?

No, you must use mange. In Danish, mange means "many" and is used for things you can count, like æbler. Meget means "much" and is used for uncountable things, like coffee (kaffe) or time (tid).

Why doesn't the verb har change?

In Danish, verbs never change to match the person or the number of things. Har is the present tense of "to have," so it stays exactly the same whether you say jeg har (I have) or vi har (we have).