For games with mandatory installs, does that mean I can play the game even tho its not in the disk drive?

No you still need the disc. But by having to install it just reduces loading times.

nope. The mandatory installs are just a small piece of data (non exceeding 4 gigs, except the revised MGS4 trophy version)

As already mentioned, no it's not the whole disc, just a few (though could still very well be hundreds of) files that a stored on the HDD, since some developers have issues with the slow reading capabilities of the Blu-Ray drive inside the PS3.

Aren't installs mandatory across PS4/XOne? Wont mind though since you can play as they install in the background.

They are on the xbone, not sure about ps4. Agree it doesn't really matter if you can play while it installs, though on disk is nice as games take up less hard drive space. The ps4's bluray is 3 times faster than the ps3's so hopefully less games will need HDD caching

Not for bluray games no.

no

Nope, the disc is still needed.