I need to use the Mouse Library (Mouse.move(), Mouse.click(), etc.) through bluetooth communication. will it work? and how? Thanks
The Mouse library makes the Arduino Micro act as a USB Mouse.
If you want something that makes an Arduino act like a Bluetooth Mouse, that would require additional hardware (some sort of bluetooth module that supported that) and an arduino library to go with it.
If you mean that you want to have a Micro plugged into a USB port acting as a mouse, and have something else connect to that via bluetooth and have that control when it does mouse commands, that has no specific concerns.
I have a bluetooth module HC-05. I want to connect the Arduino Micro to a computer via bluetooth using HC-05 then I was wondering if the Mouse.move() function and others can be pass through serial port. so it could control the computer's mouse on wireless.
The only way to get the mouse to move in response to serial would be to write a program that watches the serial port and sends mouse commands (this can be done from software on the PC). This has nothing to do with the arduino Mouse library - which is ONLY relevant when the arduino is plugged into the computer's USB port.