Regarding the transfer case, if your tcase shift lever has "4HI-N-4LO" on the bezel than it's 249 case. If its "2WD-4PT-4FT-N-4LO" then it's 242.
So, if you've got a 249 tcase, it's got a viscous coupler that's known to die by 150 000 miles. It causes both axles more or less locked together, like in part-time 4WD, which causes binding, hopping and shuddering on tight turns on dry pavement.
The options are:
- Replace with a new viscous coupler, requires taking the tcase apart and $350-450 for the new VC. Works good afterwards if you don't get a dodgy cheapo VC (some negative experience from someone here).
- Replace with a 242 case off some junkyard XJ or ZJ, fits almost seamlessly with some caveats (input gear shaft length and output yoke style), there's a huge thread on this swap pinned on top of the ZJ forum. Costs about $200 for a junkyard tcase.
Regarding the pump, check the fluid level, and check the fluid itself for bubbles in it.