Yes.
If you are interested in using Brainstorm, start by reading all the introduction tutorials:
https://neuroimage.usc.edu/brainstorm/Tutorials
Is it possible to compute other connectivity features other than correlation?
Yes.
https://neuroimage.usc.edu/brainstorm/Tutorials/Connectivity2
If not any suggestions on how to perform this on my own with any toolbox(MNE, FieldTrip, ...)?
You can also do this with MNE-Python and FieldTrip.
You'd need to learn how to write code (Python or Matlab) instead of learning how to click on buttons., but you could get to more or less the same results.
Brainstorm reads natively the Muse .csv files, I'm not sure if this is the case with the other programs.