katabana

i only have very, very, very basic knowledge on relativity, so i hope i'm posting in the right place.. i've read that the watch an observer that is closer to a sun runs slower than the observer that is further from the sun and 1st observer due to their perception of time/space, and the 1st observer actually age slower than the 2nd observer, correct? can i assume that two perfectly synchronised, perfectly conditioned watch will run with different speed because of their distance from gravity? or does the "time" that i've read refering to our biological clock, and both watches will still run in perfect synchronisation?

if thermal energy is formed when molecules are shaking and moving around within an object, can i conclude that energy = movement of molecules?