Gender often comes along with cases, which basically show you what role a noun is playing in a sentence. For example, is someone doing something, or is something being done to them. That lets you change the word order and keep the same meaning. You can emphasize different parts of the sentence, or just be more flexible with how you say things.

Here's an example from German:

• Der Hund (subject) hat den Mann (object) gebissen. / The dog bit the man.
• Den Mann (object) hat der Hund (subject) gebissen. / The dog bit the man. (Implied: That guy, and not someone else.)

In English, the meaning changes when you change the word order.

• The dog bit the man.
• The man bit the dog.

Languages do fine with genders and without. They're just different systems that happened to evolve over time. And languages can even change. English used to have 3 genders, but they disappeared hundreds of years ago. Instead of having like 12 different ways to say "the," we just have one, thanks to the Vikings and the Norman invaders.

Because äpplet means "the apple" while äpplen means "apples".

Because it's how the language works. Why do we have many, lots, large ammonts of words that all mean the same thing? Me myself and I don't really care because they are ways to express ourselves in different ways depending on what we want to convey, and how we choose to do so.

What does "a" or "an" give you in English? It's mostly historical and because it flows better.