On my 98 Jeep Grand Cherokee 4x4 limited slip when i am turning it hops like its in 4wheel drive?(just started doing this) Why?

SOURCE: 1998 and 2000 jeep grand cherokee

This Info taken from Wikipedia, the free encyclopedia
http://en.wikipedia.org/wiki/Grand_Cherokee
Hopefully this will answer your question.

The redesigned WJ 1999 Grand Cherokee shared just 127 parts with its predecessor. The structure was stiffened by PorscheEngineering for sharper steering and lighter weight. The spare tire wasrelocated from the side of the cargo compartment to under the floor togreat relief of owners. The two heavy pushrod V8 engines were replaced by chrysler's first clean sheet V8 since the 60's (SOHC aluminium heads, plastic intake), Chrysler's then-new PowerTech. Although this engine produced less torquethan both previous V8s, it was lighter and got much better fuel economyand provided similar on road performance figures (the 23 gallon fueltank was replaced with one of a 20.5 gallon capacity). The Inline 6engine was also updated in 1999. 10 horsepower (7.5 kW) was added byredesigning the intake manifold. The manual transmission was dropped with this model.
While other Jeep vehicles used the Mopar 5 x 4.5 bolt circle, thiswas the first Jeep following the 1987 Chrysler buyout to receive awider bolt pattern — 5 x 5. The 5 x 5 bolt pattern (also 5 x 127 mm),although common to GM rear wheel drive vehicles and light dutytrucks/vans, has spread beyond its use with GM (and Ford with their 1973 to 1978 LTDs and Lincolns). Chrysler first used the 5 x 5 pattern on full-size half-ton Dodge Ram pickups and Dodge Ramcharger SUVs in 1986.
A notable feature available in this generation was the automatic four wheel drive option called Quadra-Drive II.With three viscous clutches, it was one of only a few four wheel drivesystems at the time with triple locking differentals, joining thecontemporary Mercedes Gelandewagen, Mercedes Unimog and Magna SteyrPinzgauer, and the only one of the four with fully automatic operation,although the axle differentials could not be manually locked like inthe other three vehicles.
The 45RFE and 545RFE automatic transmission in the WJ was notable. It included three planetary gearsets rather than the two normally used in a four-speed automatic. Thisgave it six theoretical speeds, and it would have been the firstsix-speed transmission ever produced in volume, but it was programmedto only use five of these ratios. Four were used for upshifts, with adifferent second gear for downshifts. Although five of the six ratioswere used, Chrysler decided to call it a "4-speed automatic". In 2001,the programming was changed to make use of all six ratios. Rather thanhave six forward gears, the transmission was programmed to act as afive-speed with the alternate second gear for downshifts. The RPM at70 miles per hour (110 km/h) on a 545RFE is 2000 rpm, 200 rpm less thanthe 45RFE programming. 1999 and 2000 model year WJ owners can havetheir 45RFE transmission's programming flashed to enable the extra gearas both transmissions are physically the same. The 42RE 4-speedautomatic remained the transmission for the Inline 6 engine. It was notchanged from the previous model Grand Cherokee's.

SOURCE: 2000 jeep grand cherokee limited starts in 3rd gear

oil pressure problem should be checked independently of other problems...Use a good accurate mechanical gauge to check. If pressure is good (no less than 15psi at idle hot (I prefer to see at least 20) check dash grounding, block ground and if OK, change sending unit. Dash and body ground can influence operation of shift and body control modules so indirectly your problem may or may not be related, depending upon what you find while testing. And it could turn out to be a defective module! They are expensive and just plugging new ones in may work, but then again, it might not. I might be totally incorrect on this...that's the value of actually being there instead of doing this by "remote control".
If you read the numerous posts pertaining to all vehicles, you will see that you are not alone with electrical problems...As long as the engineers who design this stuff, keep using "modules" to replace ordinary simple and reliable systems, we will continue to have these problems. Do some testing and I'm sure you will find a solution! (I'm still waiting for someone to make a program for a PC that will give a complete readout of every system in a vehicle, including exact faults instead of general system "suggestions")
Good luck

SOURCE: 1999 jeep grand cherokee all time four wheel drive will not engage

Sounds like the splines on your transfer case gear are ground down

SOURCE: jeep grand cherokee slow to start

THE THINGS YOU MENTIONED WON'T AFFECT CRANK SPEED. YOU'RE BATTERY IS PROBABLY ON THE WAY OUT THE DOOR. LOOK FOR CORROSION AND LEAKING BATTERYLIKE AROUND TERMINALS AND POSTS. BATTERY IS PROBABLY LOW ON CCA'S. NOW IF TALKING ABOUT WON'T START AND TAKES LONG CRANK TIMES IT CAN BE FUEL PUMP LOSING PRESSURE IN FUEL RAIL OR LACK OF FUEL PRESSURE CONSIDERING WHAT YOU MENTIONED. EVAP SOLENOID WILL USUALY SET A CHECK ENGINE LIGHT AND WONT AFFECT STARTING USUALLY UNLESS YOU HAVE A HUGE VACUUM LEAK

SOURCE: 98 Jeep grand cherokee limited 4.0 auto gearbox shift down

Throttle position sensor