I don't think it should be a problem at work as long as you talk in private. It seems like it could be beneficial for both of you. You know what the other is going through. It's great to know there's someone to talk to. Of course I don't need to tell you that. I'm not sure what words and descriptions you might have to change though.
As for the clothes, speakinng for myself, I wouldn't say no to hand me downs if I were friends with a FtM at work. I wouldn't consider it rude, more a nice gesture. One which I would probably return. But that's just me.
