Aim at, Aim for, Aim to
Hi everyone! I'm struggling with the meaning of these words.
I have already tried to learn how to use them but I have still issues.

Here there are my examples:

I want to throw a piece of paper in to ( INTO?) a basket.
Whoever get the basket first wins.
- We are all aiming at/for the basket.
- We aim for the goal. FIGURATIVE
- Someone stops this man! He's aiming the knife at those poor children.

- We aim to win the rich prize.
- We aim at winning the rich prize.

Thanks to hoever spend their time to correct my mistakes.

Question

Aim at, Aim for, Aim to
Hi everyone! I'm struggling with the meaning of these words.
I have already tried to learn how to use them but I have still issues.

Here there are my examples:

I want to throw a piece of paper in to ( INTO?) a basket.
Whoever get the basket first wins.
- We are all aiming at/for the basket.
- We aim for the goal.              FIGURATIVE
- Someone stops this man! He's aiming the knife at those poor children.

- We aim to win the rich prize.  
- We aim at winning the rich prize.

Thanks to hoever spend their time to correct my mistakes.

Answer

There are three uses here.

aim + infinitive
We aim to finish the bottle. (we plan to finish the bottle. We have an objective of finishing the bottle)
Our aim is to finish the bottle

aim for
When shooting a free throw, aim for the back of the rim.
The hunter aimed for the bear's head.
Messi aimed for the upper right corner of the goal, but his shot bounced off the post.

take aim at

The sniper took aim at his target, but was killed before he could get his shot off.
The newspaper took aim at the politician because he attacked freedom of the press.

You can't really "aim" a knife, unless you were planning to throw it.
Let's play a game. The first person to get his paper in the basket wins. (in my opinion, trying to throw something into something isn't a good use of "aim". You could "aim" for a part of the basket though.)