compatibility of Bluetooth module and Android devices
It depends what kind of data you want to send. The Android will support any bluetooth profile listed on the developers site for the respective versions. I found some info here. Most common profiles will be supported. Then you just need a module that supports the profile you wish to use.

If you want to implement a UART type connection, then you need the SPP (Serial Port Profile). Many cheap modules are available which will do this, I personally use the HC-05 module for a few of my projects. You can get modules that connect to the uCs UART, SPI, and USB ports.

Other commonly used profiles are audio (A2DP), HID (Human Interface Device), etc.