Does Basic ESC have a voltage regulator?

Nope, no voltage regulator is included.

That’s incorrect. As per the technical details the T200 is rated for 7-20V powering (so your 14.4V battery should work fine, assuming it has the current and energy capacities you want/need). In addition:

If you choose to go ahead with the above-rated-voltage battery without using a regulator, there’s information here that can help you set a hard limit on the commands sent to the ESCs, to reduce the chances of the thrusters getting damaged.

EDIT: I’ve just seen in your other post that you’re making a boat, so may not be using ArduSub to control it. If that’s the case then the same principal applies for limiting the PWM signals that get sent to the ESC, but you would need to set that up yourself for the system you’re using.