I'm pretty sure we exceeded the 1000 object limit a while ago and are still going. Really, it comes down to drive space and general hardware as to what the upper limit is. however, I would assume that 1000 is on the low end.
To answer your other question... no... per project, there is only one NameMapping file per project.
As mentioned elsewhere, though... Extended Find is probably the primary culprit in your current performance woes... Go through your existing mapped objects, turn off the option where it is not strictly necessary, add any missing ancestor objects, lather, rinse, repeat. You'll see a MAJOR performance improvement, I'm sure.
Yes, I have turned off extended find and I have restarted all my mapped objects in a brand new project.
May be a bit drastic... you don't necessarily need to delete all your mappings and start over... I'll leave it up to you to determine which is more efficient but you can "correct" your existing mapping to add in the missing ancestors.