I have a 2000 Xterra and driving it. It started

Easiest way i kniw to donit is crawl underneath use ya cables n hook to the battery side on the starter the one xable leading from the top that will power your system to open ya doors and start it

Tires...rear suspension...rear alignment - in that order. I had a car with a really bad rear alignment that hop sideways every time you went over a bump in the road.

Possibly but to find the fault have the fault codes read . It may be the accelerator position sensor . Don't waste money until you have the codes to point you in the right direction

it sounds like it jumped time check your belt or if it has a chain check the tensioner.

Check the source of the oil and gas,
Oil pan,freeze plugs, exhaust manifold and muffler are potential sources.

if its the whole car doing it not just the motor check the tires. if tires are out of balance or warped then typical they will buck or jump from 50-60 maybe 65 mph

check the u joints in the front drive shaft

Does your actual speed change or just the displayed speed? It could be a build up of brake dust on the speed sensor behind the rotor if it's displayed speed.

did you have a compression test run.

When was the last time you shifted to 4WD?

If you do not use 4wd too often then try this old trick.

Next time you're going off road try to do the shift to 4WD,shift to reverse and drive in reverse for 6-12 feet.
(no gas //1 mph //SLOWLY)

Driving backward for few feet help the gear pickup the lubrication and let the gear sync up better.

Check your Xterra gearbox lube schedule.