First off, let me apologize for the newbie question; my experience with hardwood to this point has only been new construction, and small areas like entries and kitchens, I've done a few large jobs, but again all new construction.

OK, I've got a customer who is rehabbing and old home. There is no subfloor, just the existing original 3/4 hardwood directly over the joists. Is this a suitable subfloor to lay solid 3/4; if so do I just run it perpendicular to the existing hardwood? If it's not suitable, what must be done, can I lay 7/16 osb over it, then lay the hardwood? Please, any guidance will be appreciated.

Opposite direction, or 45º, or you can overlay it with plywood and go back the same direction as it is now.

Thanks.

In these situations, are the old floor boards usually installed pretty firmly, or do you usually need to go screw it down to the joists tight for better stability and to minimize squeeking?

Sure, if that helps reduce the squeaks.

I'm not sure, I have not yet checked the floor for squeaks.