As a guitarist, if I'm playing with a pianist, I usually do a couple of things.
If I haven't played with them before, I'll usually lay off a bit in order to get a feel for how the pianist wants to approach the comping. I tend to adapt my paying around my bandmates when I'm comping.
If the pianist wants to do some complicated rhythmic stuff, I tend to go ...
This is a tough call. Where on the finger board is not really helpful. The bigger issue will be two people comping simultaneously and having the rhythms clash. Do you have a Bass in the group? If not you could always play a sort of walking chord melody bass line in the lower register. That would fill up space and keep the steady groove going and act as ...
I play piano myself, and I recently played with a trio with guitar and bass for the first time.
My experience, as a piano player, when having a solo, was that the tight, clustered left hand chords (Bill Evans) worked not so well with the guitar comping underneath. The alterations may clash, especially when the guitarist used tight voicings of his chords. ...
Don't play full 6 string chords, but partials (look at the LCJO tutorial on YouTube).
Don't play all the time.
Listen a lot.
Listen some more to the Nat King Cole Trio with Oscar Moore or John Collins.
Find out where your guitarist likes to play on the fretboard, then go to a different register on the piano keyboard. What to do will be very different if the guitarist wants to play open-string voicings or spend most of the time somewhere above the 12th fret, an octave higher.
There are a few things he's doing with the rhythm. I'm not sure if there's a name for the whole effect, though.
The slaps happen on beats 2 and 4, constituting a backbeat.
There's a chord on beat 1 and a staccato chord on the last 16th note of beat one. This is sometimes called an anticipation.
The bass thumps are on the last 2 16ths of beat 2, stopping ...