I used a third party application to try and clean up space...and it somehow deleted iPhoto entirely. Now I can't get the application back. Advice?

My advise would be don't use 3rd party disk cleaners unless you're sure about what they are deleting! lol

I'm guessing you don't have a TM (or other) backup... Is the problem that you can't get your photos back, or the program (or both?) If it's the photos, I'm sorry but I think they might be lost if you don't have backups (though you could try some sort of file recovery/undelete program - I've used them with some degree of success-about 50% I'd say- I forget which program(s) I ended up using, but one name I remember is FileSalvage.)

If it's the program that you can't get back, is the problem that it won't let you reinstall? Or do you not have the reinstallation media? If it's he latter, I'm sorry but I think you are out of luck and will have to obtain another copy. I might suggest the new Mac App Store (especially since you can always redownload from there once you make a purchase. I've never tried Aperture, but I hear it's much better than iPhoto and is on sale in the App Store.) If it just won't let you reinstall, what error are you getting? Maybe search your system for any remaining iPhoto stuff, and delete it first?

My final advise would be to start making back ups of your system. You can get a 1TB external drive for under $100, and it's so easy to set up backups in Time Machine and once it's set up you don't need to think about it!