I have a harbor breeze ceiling with a remote that was never wired in.can
I reverse the fan direction manually.

Is there a question?

I can help, if you give me more information. You already edited your original post tpo provide some, so I can say this:

If the fan has pullchains for independent control it likely also has a reverse switch somewhere on the fan body. If it is designed to be controlled from the remote then it may not.

No you cannot. You must have the right receiving unit installed (the one that came with the fan) and the right Harbor Breeze hand held. If you don't go to Lowe's for parts. Wiring things up is pretty easy.

No you cannot.

Yes you can, depending on the fan and the control configuration.