Control/Interacting with Android OS using Arduino board
What you've seen is most usually a bluetooth module which has a "virtual COM port" service -- you connect to the bluetooth module and you can then send a data stream up and down through this COM port, just like you are able to do with a normal Serial port.

If you want a bluetooth keyboard:

What you want for seamless integration is a bluetooth module which natively exposes a "HID" (Human Interface Device) profile. Keyboard, mice and gamepads are examples of an HID. 

There is a multitude of projects which use Arduino + Bluetooth HID module:


http://www.kobakant.at/DIY/?p=3310 uses an Arduino Pro Mini and and BlueSMiRF HID (from Sparkfun)
Evan Kale's video: https://www.youtube.com/watch?v=BBqsVKMYz1I (uses HC05 bluetooth module with altered firmware)
https://mitxela.com/projects/bluetooth_hid_gamepad
Bluefruit EZ-Key: https://www.adafruit.com/product/1535


When you are a beginner you should buy the more expensive modules which don't require you to do any firmware hacking. Adafruit's product might work for you. As the description page says, you can connect a microcontroller's UART TX to the modules RX pin to send arbitrary keystrokes. You can then add a keyboard matrix, or lots of buttons, or whatever you desire to that microcontroller to make it trigger the keypresses you want.

This should get you started on your own research.