If I have partitioned my hard drive, can files in one partition harm/access ones in another partition?  I'm wondering if a partition 'contains' the files in it I guess.

Partitions are used to keep files seperate but if file is a virus then in theory it can affect any part of your computer.
 
Depends on what the file is  

Boot Sector Virus, anyone?
 
If you're trying to 'contain' a potential threat, look up 'virtualization', or more specifically a little program called 'Sandboxie'.