The most common reason for rain shower heads to drip is due to the shower heads clogging over time, caused by limescale deposits as well as other minerals and bacteria.
Essentially, the congregation of these minerals and limescale can lead to the small holes that feature on the shower head being blocked and unable to distribute water as effectively. In turn, they can drip when the power supply is switched off.
No, not all taps will be a suitable fit for all baths. Typically, your bathroom fittings and fixtures will play a part in dictating which taps can accompany them, in addition to your own personal preference.