Yes, you can play NTSC games on Xbox 360. There are some restrictions, but most games should work fine. For example, Madden NFL 09 and NBA 2K10 will not work correctly because they use the PAL format for their game clock. However, most other games should run without any problems.
Yes, PAL consoles can play NTSC games. However, some games may not work properly or may not be compatible.
The Xbox 360 is region locked and cannot be played on PAL systems. There are a few methods to get around this, but the easiest is to buy an Xbox 360 copy of a game that is available in both PAL and NTSC versions, or use a modchip.
There is no universal answer to this question as it depends on the specific game and region. However, some games may work while others may not. Some common issues include PAL games not recognizing the controller or the console not being able to read the disc.