Yes, but generally this would be used the opposite direction. If cloud bases are unavailable, or if weather is changing rapidly, you could use say barometric pressure + dew point to determine "is this about to go south towards low clouds and low vis?"
(Also, cloud bases are part of the METAR info in the first place, so it's a "neither" situation)
I remember being the other way around, you could estimate height of the cloud based on dew point and base altitude.
Yup! 400' AGL for every 1 deg C of temperature spread.
Yah! So you can find the dew point by flying up to just below the cloud and look at the altimeter and do some math ;)