App and photo editor
Apps are easy. He just needs to authorize his new computer with his iTunes account and all the apps will transfer over to the computer without a problem. I think if he "checks for downloads" in iTunes, it may download all apps he's purchased as well.
For the calendar, he needs to create a dummy event in outlook. Then when he syncs his iPhone, iTunes will ask if he wants to replace the computer, replace the iPhone, or merge. Select merge, delete the dummy after the sync is complete, and sync again. The same idea holds for contacts.
Since he is jailbroken, there may be other options but I'm not familiar with them.