Well, as for the door opening slowly, its the gears, they arent aligned correctly. there should be a little pin that you can pull out and it lets the whole tray pull out. After that you can just slide it back in.

The Tray not being aligned properly may have to do with how the disc is inside the PS2, so the laser may not be hitting it. Did anything happen to it to make it do this?

EDIT: Heres a link to a thread at PCApex when I had some console problems:

Seeking Console help - PCApex Forums