Didn't you answer your own questions? She did it to be special. I reckon she sees Kumiko a bit special as well due to her bitchiness behind the polite facade. Kumiko was first interested in her, which means Reina could be just using Kumiko for practice and as an outlet as well. The mountain climb was a single, straightforward event, so she could have planned it all out beforehand, and then just followed that script. It's special, after all. If she really wants to become a special musician, it works much better if her whole personality has some peculiarities as that would make her memorable. She just needs the guts to develop herself into that direction. Based on this ep, she has what it takes, at least for now.