iTunes updates
When I download new apps it asks for my password. When I try to update apps it asks for the previous owners password. Why is this
It would seem the previous owner did not correctly wipe the iPhone clean, and left Apps tied to their Apple ID on there.
Apps are forever tied to the Apple ID that downloaded them, and will forever require it when updating it.
If the previous owner did not correctly wipe the device, it may lock you out at any moment if his Apple ID still signed in to iCloud on it.
Its for that reason that the previous owner should have followed the steps here to completely clear the device:
What to do before you sell or give away your iPhone, iPad, or iPod touch - Apple Support