What does "professionally installed" mean? Maybe find out what shop did the work and then google-search to see if they seem to have a good reputation.
Mudding = twice/ rock-crawling = twice? Not very likely. Very few people are going to disclose anything more than "once or twice off road" because there is seldom going to be any way to dispute this. That doesn't necessarily matter.
What matters more is how it drives/ how it handles. What noises ( if any) do you hear when behind the wheel driving slowly around town/ on the highway/ and while flexing a little bit... Grinding, vibrations, strange thumps, etc, etc... will tell you some more about the condition of this rig.
What kind of maintenance was done on the rig over the 50k mile life so far? What kind of receipts does the owner have? How often was the oil changed?
Look under the rig when you go to look at it. Look for signs of any fluid loss/ leakage and see what kind of condition everything is in... including any and every thing that you can think of... air cond, heat, wipers, cruise, auto windows, door locks, bushings, control-arms, suspension components, serpentine belt, hoses, etc, etc. Check the oil on the dip-stick to see if it's dirty and how varnished the stick is. Doesn't mean that there is a problem if things don't look great but might provide a little more insight into past or potential problems. Does it have a hitch? A quick inspection might tell you if it's towed anything throughout it's life.
It's not too hard to get a decent idea of someone's integrity during a potential buy so read the seller as best you can. If you find him to be not answering questions or double-talking, outright lying, etc... then that should be a red-flag.
Also not hard to quickly evaluate how clean the rig is inside and out... including underneath and in the engine bay. Hell... look at the air filter. If it's super dirty then you know right there that maintenance might not be up to required scheduling.
Take down the vin # and see if you can find any additional info on it... accident, repo, # of owners, title status, possible flood damage, etc, etc, etc. If you can take it to a qualified mechanic, then do that too.
I don't see anything that you've listed as something that would affect my interest if it was me, but I would however, go ahead and do as much homework once you're in front of the vehicle as what you can.
And as always... find legitimate reasons to lower your offer from asking price. Good luck.
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