you wouldn't want to. yes, you can store more, but you have to uncompress it when you use it so It's slower. just get a larger hard drive...
Your psp would need to be able to read compressed files (like ZIP, RAR), which I doubt it can. TO compress them though right click > send to > compressed/zip folder
Yeah can the PSP read those? Good question to answer. Use WinRAR or WInzip like exchange said, when you drag drop or add the files into a zip or rar folder it will ask you what you want to do and what compression mode. Just select compress to the smallest amount.(I think it's "best" in winrar)
Also I just remembered you can compress but not zip (even though its not the most useful) by right clicking, hitting properties, then click and advanced or attributes button, and select the compressed option then ok. something like that