Why 2.35cm? Presumably you mean 2.35 inches. Well, I've never used them. The only reasons I can think of is if you are a downhill mentalist or just like going slowly.
As Karlos stated you have a greater contact patch and therefore better grip and better puncture protection. Ideal if you ride a lot on rocky trails.
Why 2.1cm? 2.1 inch, a fairly normal tyre size that works fine.
Correct 2.1 is the general racers tire width (pros prefer 1.8 or even some like 1.7). Good rolling tire width but less stable in gnarly sections and a higher risk of puncturing.
Why high tyre pressures (over 35psi)? To go fast
Correct. But at a loss in traction on technical sections/corners. I actually ride with 40psi on most of my tires but that is because I like to go fast.
Why lower tyre pressures(under 25 psi)? To get pinch flats.
I find that riding with tires under 25psi the tire tends to deform too much sending you off line.
Why tubeless? Less weight, lots of disposable income.
Tubeless tires give you several advantages. Pinch flats will generally become a thing of the past (but not impossible to do). I have been running tubeless for several years now and I generally get one puncture per year as apposed to one per week when I was using inner tubes. If you do get a thorn puncture for example the sealant you put in the tire will fix it before you even notice. Plus you don't get sudden flats so often as you do with inner tubes as the rubber doesn't stretch to make the hole bigger as with inner tubes. The other major advantage is the tire seems to make better contact over the terrain.
Why reverse the tyre direction? Useful to extend the life of worn tyres.
A lot of tires are designed to run in one particular direction.
Preferred tyre thickness for winter/muddy conditions? 2.1 inch
There are two schools of thought. One a fat tire sits on top of the mud better a thin tire slices through the mud better.
Preferred tyre thickness for dry/summer conditions? 1.95 inch
Rubber type and amount of knobbles have a greater sway on how the tire performs than its thickness.
Preferred method of puncture protection? Steering around glass etc.
Tubeless with a sealant in the tire.