Ceiling Fan Remote Wall Control Hampton Bay Harbor Breeze Litex UC9051T REVERSE

I have a minka aire fan. the controller has minka aire on it, but on the side it show model uc-9051t. will this work to replace?

is this wall control compatible with my litex winsong chq8bt7030t fan/light remote control, or different?

Does this work with the existing fan receiver that uses a UC7080T remote?

Will this work with the harbor breeze beach creek fan model tg44lw3d1rc. we already have a reciever as well as the remote that comes with.