What PS3 firmware is on your Slim? If it's anything above 3.41 your not gonna be able to use the exploit (yet) I'm afraid...
But to answer your questions:
1. You won't be able to use your old computers HDD unless you take out your PS3s internal HDD and swap it with that. I'm sure you have plenty of space for some games to fit on the internal one. If it's getting full just erase some
2. To run .PKG files, just put them on a regular USB stick and pop them in your PS3 (After you jailbreak it) then just go to 'Install package files' and install the .PKG.
3. Yes. You can copy games that are bigger than 4GB using FTP. And no, FTP won't damage anything. Worst case scenario you'll just have to re-copy the game again if it gets corrupted for some reason.
4. If you update. You can't run your exploits. So I'm afraid you can't go online... for now.