Yup you can play PAL games with NTSC bios and NTSC games with PAL bios. That is as long as its a good(uncorrupted) bios.
scph1001(this is NTSC) and scph7502(this is PAL) are the recomended bios, but it doesn't matter which you use except for one or two games that some people have trouble running without a certain bios.
You already know. The difference is mainly due to the different regions. As for the different files from the same reason that's for adding extra features and bug fixes (eg the original jap playstation did not have a fully working country check hence the swap trick).
Yes you can use pal games on a Us Bios, just as a mod chipped psx can run imported games.