bad mood - If I didn't want to be specific (angry, depressed, frustrated) then I would sign bad and then fingerspell mood
don't care - I use that sign no matter who I am referring to - me, he, she, them - but if it is someone else, I do the sign a little further away from my body closer to where I signed he, she, them.
that makes no sense - I would sign, "means what that?", or "don't-understand what say you", or even "crazy that" (if that was my opinion about what they were saying haha)
Be patient with yourself, learning ASL structure takes a loooong time and lots of exposure to the language. I suspect I will learning for the rest of my days haha because even in the community itself some sign strict ASL structure, some sign PSE, some sign somewhere inbetween - personal preference plays a big role and it depends on what kind of environment they grew up in and now live. Best advice I can give (for what it's worth), don't ever stop asking questions, don't ever assume there is only one way for something to be expressed.