I have two problems. They both appeared at the same time

Problem #1: The following programs some how ended up in my trash bin. System Preferences, System Profiler, Safari, HP Device Manager, Directory, Grab, Folder Actions Setup, Preview, Digital Color Meter, Mail, and Itunes. The Icons were still on the bottom (I guess this is the dock). When I would click on them a message comes up telling me they are in the trash. I need to retrieve them from the trash. I grabbed them and pulled them to my desk top and they work. I want to remove them from my desk top.

Problem #2 I keep all my music on an external hard drive. I actually have it backed up on two separate hard drives. I have 56gb of music. As I said this problem occurred when problem #1 happened. When I have both or either hard drive connected all my music shows up in the trash as well as Itunes. The music play fine and uploads to my Ipod fine. The problem is I can nor delete anything in my trash can with out deleting every thing in my trash can. If I eject the hard drives the music in my trash goes away. Can someone please help me with these 2 problems