It does not matter who do you host with. You can do link from A site to B site. It does not count as linkback but traffic referral to B site (traffic referred by A site).
Of course it counts, but from limited experience, I suggest you not do to that, Google does’t like link wheel thing, especially when all of those websites on the same hosting. I might be wrong, though.
Search engines will count them if they are relevant to each other… If you are linking an e-commerce website with a law site that makes no sense and search engines will drop the backlinks.