I have been told that some of these things could be achieved using promotions however will that require my moderators to manually approve each post the new user makes before he reaches the minimum amount of posts let's say 20 posts?
No, you just make a user group that everyone is initially placed into (registered) without those permissions, then create a user group that does allow those permissions (whatever you want to name it) and create a user group promotion that has the necessary conditions that a user would have to meet in order to receive the promotion. No manual moderation should need to be required, that is completely separate
I take that back partially, you can do everything you want with permissions and promotions except the links. There is a permission for signature links, but not post links. I know that TAZ has something installed to prevent links until you have met a certain criteria... @The Sandman might be able to tell you on that one