Many of these English translations are grammatically impossible, especially when it comes to motion verbs.

For a verb like "sit", English usually can't distinguish motion from state: "The children sit in the garden under the tree and play." or "The children sit out in the garden under the tree and play."

With an explicit motion verb: "The children go out and sit in the garden under the tree and play."

Likewise, in English, it's very unusual to say that a person "sits into a chair" (this is in reference to an earlier exercise). You can "get into a chair" or "sit down in a chair" or just "sit in a chair". But "sit" doesn't like to take prepositions of motion.

"Sit out into..." is not correct English in my opinion

This answer is very awkward and it looks like a literal translation.

I'd rather say "The children are sitting under the tree in the garden and they are playing".

There is no need to even mention "out" - if you are in the garden you can't be inside.

I agree. You can go into the garden but you would sit in the garden.

The children sit out in the garden and play under the tree. Means exactly the same thing as the accepted answer in English.