If you have an external disk attached and empty the Trash on OS X, it will also empty the trash on the external disk, i.e. files that you have trashed from the disk while it was connected to a Mac. This is where your 60,000 items come from (most probably).
The items are in a folder called
.Trashes on the volume, inside another folder with your user id. As it, per default, this should be 501. Try opening Terminal.app from /Applications/Utilities and enter:
Just replace "your-external-drive-name" with the one you see in Finder. Then you should see the trash content.
Can I copy & use applications/extensions (iPhoto, Firefox, Picasa, Flickr, etc.) and safely trash them from the main OS X hard disk?
You can copy applications to another volume and open them from there. I would however not do this with applications that come with OS X, such as iPhoto. Note that you might also run into trouble with the application's preferences correctly being stored or any interdependencies. I have not tried this yet and I honestly don't think it's such a good idea.
That being said, it works okay for small standalone apps – should definitely work with Firefox – but I wouldn't do this with bigger ones or at least test it out before you delete anything for good.
Note that moving applications to save space is probably not the best idea. There must be something other that fills up the space. Use a diagnostic tool like Disk Inventory X to see which files take up your hard disk and delete those.
Can I use the external drive as my main hard disk, so free space will no longer be an issue? Either move, copy or connect entire OS X system to the external HD.
You can run OS X from an external drive alone. This however will result in a bit of a performance loss, as you don't have the same read/write rates as with an internal disk. Not really recommended for daily use.
I would strongly suggest you buy a new internal hard disk for your Mac. Hard disks are very cheap these days and you can easily make a backup of your system with Time Machine. Then, when you have a new hard disk, restore your Mac from this backup.