"01. Is it necessary to have same IOS version running in all the stack members in order to create a stack? If not what are the limitations that are there when using different IOS versions?"
For the 3850 switches, I believe the answer is same version and feature license.
For the 3750 switches, unsure if same applies to 3750X series, but the original 3750 series, and the -E series too (?), could mix feature sets, and even IOS versions, but when mixing IOS versions, the "major" StackWise version has to match, but "minor" StackWise versions didn't have to match. Generally, sure bet was to use the same IOS version within a stack, but I dealt with mixed feature set 3750 stacks w/o issue.
"02. Can we create a single stack using Catalyst 3750x switches and Catalyst 3850x switches?"
To my knowledge, no. You can mix models with the same family. For the 3750s, you could also even mix the original models with the -E and X 3750 series, but that also caused the later two series StackWise+ to run in StackWise mode. Also, with the 3750G-12S, it had SDM templates unique to that model (designed, and with resources, for a distribution role), i.e. only to be used in a stack with like models, but it also supported the "normal" SDM templates if you were going to use that model with other 3750 switches (in the stack).
