For some reason my moderators can't delete posts. When they try to delete somebody's post, it says "you can not delete other members' posts".

Also is there a way to make it so when a moderator tries to delete a post, it automatically moves it to the basket instead??

You need to go to Admin Panel -> Forum -> Permissions and there you can modify your categories and forums for members, moderators and other.

You can't delete towards the basket only for posts, you'd have to split and then garbage

so to allow them to delete other's posts, I have to check "allow deletion of own posts" or whatever it says?