In the west, we have to deal with people who belong to the LGB2Q…(etc).. community. My question is: if I have a lesbian woman as a classmate where we have to do class activities that require touching and exercising together, is this ok and halal considering her interest in women.

Another question, should I observe hijab in front if a transgendered woman?

Yes you should observe hijab and try to avoid any activities that you described