NO, you cannot use regular recessed cans as heat lamps. You need a heat lamp fixture. Most have a fan built in with a thermal cutout so if it gets too hot either the light goes off or the fan comes on.
Bath fan companies make them.

Yes, you can use 12/3 to run two circuits.
NO, you cannot re-feed a 14/2 circuit with the #12 and use a 20 amp breaker. Using #12 would be a waste.
Just leave the existing as is and run new circuits to where you need them.

Regarding using a 3 wire to supply 2 new circuits to bathrooms being gutted..I just read another post where the GFCI keeps tripping because it shares the same neutral. Is this going to be my situation that I will have 2 bathrooms with seperate circuits being feed from the same neutral on the 3 wire. I did not fully understand the post. If this is the case, can I install a GFCI outlet in the bathroom, does this eliminate this problem? I will have a bathroom light and fan over the shower too which I need to get into the GFCI circuit.

If you split the circuits to two 12/2 feeds you can do as you wish after that as far as GFI devices. There will be no tripping problems.

The fan over the tub should be GFI protected only because the manufacturer most likely requires it. There is no GFI requirement for recessed lights or fans OVER tubs. Only that we follow mfg instructions.