A large number of old XBOX1 games will play on the 360, but not on the CORE model as you have to have the hard drive attached and download the compatability updates. There is a list of whats compatible on xbox.com
With regards to importing US 360 titles....a lot work, but not all. Its down to the publisher to decide if they want to make their games multi region, so the likes of EA allow none to work, but MS themselves don't mind. You can look at a website called PlayAsia to see if a particular US game is going to work.
Going back to XBOX1 games, with regards to imported games working, there are very few US XBOX1 titles that will work on a UK 360 in backwards compatability mode....so few that its effectivley none.
Hacking the 360 makes no difference to its region locking satus.