do larger planets should rotate faster and the interior of the central star should be hot?

Answer 1

larger planets tend to rotate slower than smaller ones and heat is a product of gravity so the larger the body (planet, sun etc) the hotter it is

Answer 2

Jupiter, our Solar System's largest planet, does rotate faster than all the rest. This is probably because it is so big, that nothing (asteroid & comet impacts) has been able to slow it down. On the opposite end of the spectrum, Venus rotates so slow that its day is longer than its year, and it rotates "backward". Venus probably got hit by something big (or several somethings) that changed its rotation - it almost certainly started with a fast rotation like Jupiter's.

By definition, a star is an object that produces energy by nuclear fusion in its core. Since the energy production is at the center, the center is the hottest part of the star.