1) The answer depends on what specific wireless enabled MCU you are using and what standalone MCU and standalone wireless module you are comparing it to. In general, I would expect an integrated module to be more efficient as there is more opportunity for optimisation. I am not familiar with BLE so I can't comment on it specifically or on modules in the market today.
2) RSS is sensitive to noise and interference (exactly how sensitive will be depend on the exact PHY implementation of BLE you are using) so what happens in the environment will cause fluctuations in the RSS value. This is especially true with PHY layers like BLE which use the popular 2.4GHz.
If you want to perform RSS localisation you have to accept that there will be errors introduced by these fluctuations and also possibly by the inaccuracy in estimation of the RSS. Instead of basing a localisation estimate on a single RSS value you might want to consider taking several measurements and then filtering them (perhaps by using the Kalman filter) before making localisation decisions. There are many RSS localisation schemes that you can look at and decide which will work for you.
I don't know the exact algorithms you are comparing but in general RSS fingerprinting based methods will be more accurate than just doing blind triangulation but then again fingerprinting is much more restrictive as the fingerprints have to collected and stored or delivered to the device. In addition devices relying on RSS fingerprinting will be limited to operating in a set area.