1. Whether its possible to calculate the distance from a transmitter to a receiver
You can get a bluetooth to determine if another bluetooth is in range - whatever that might be - but, for anything else, I think you are just kidding yourself, and a piece of string would probably be a better option.
You might find the following entertaining
- Would be able to point me in the right direction to look for transmitters to experiment with
The Tinysine HM-10 modules would be a good choice. They are dirt cheap, easy to configure, and have a range of 30m or so. This latter is because they are BT-4 type. Note that a BT-4 device only operates as BT-4 when it is working with another BT-4 device. If it isn't, it reverts to plain-vanilla BT-2. Another is the ever-popular HC-05, but it is BT-2 and is probably about to be superseded by the HM-10.
- Could recommend the best current BT library to start experimenting with
You don't need any libraries. Bluetooth is just serial without wires and Arduino is not involved.
- Point me in the direction of some good info to get started
The following background notes are not quite what you want, but may still be useful.