Can I mix shifter (deore m4100 10 speed) with my Rear Derailleur (deore m6000)? Can I use deore m4100 10speed shifter with my RD deore m6000 10speed RD?
Yes, all Shimano mountain 10 is the same actuation rate for rear derailleurs as can be seen in the compatibility chart:

Note that 9, 11, and 12 are all different, so speed generation mismatches are the thing that doesn't work.