I wanted to develop an android game that is a 3d plat former with Bluetooth capability so that players when near each other can compete to the finish line. So is this possible with Unity3d and also when I download the free version will I also get the android development kit along with it?
Android development is free since Unity 4.2. For Bluetooth multiplayer, you can use this asset: Android Bluetooth Multiplayer.
It is designed to be compatible with Unity built-in multiplayer, so you can use any of existing tutorials about Unity built-in networking to make Bluetooth multiplayer.
3D platformer is definitively possible with Unity!