What is the acceleration of the stars' speed in the Universe? Positive or negative? I have read quite different opinions about that, so can someone tell me what is the sign of the acceleration of the stars in the Universe if we accept that the center of the Universe is the beginning of the coordinate system? At least what is considered as correct finally :)
This is the classic misconception about the expansion of the Universe: there is no center of the Universe. The whole universe expands as one, not from a single point nowhere.

Knowing this it makes no sense speaking of the direction of an object due to the Universe. You could compare the directions of two objects in it though.

Therefore star's direction depend on where and how they where created and also the interaction with other stars and their home galaxy.