Are Declination and Right Ascension values (more or less corresponding to a celestial latitude and longitude?) always relative, changing according to the relative position of bodies in space, or are there exceptions? For example, regarding the stellar bodies, do they not have a characteristic, absolute position on the celestial sphere?
Right Ascension (RA) and Declination (Dec) work exactly as if they were a kind of celestial longitude and latitude, based on a certain reference system. All celestial objects are in motion relative to each other. Therefore, the respective RA/Dec change with time. However, for distant objects such as stars, this change is so small that it's only noticeable to us after many years. For this reason, we were able to identify figures formed by the stars that seem to remain unchanged in time. However, after thousands of years these figures will undergo progressive changes.
An object closer to Earth, such as a planet in the Solar System, has a much more perceptible movement under the celestial sphere. In the case of the closest planets, we can see their displacement from night to night on the apparently fixed background of stars. In the case of the Moon, which is right next to us, its movement in relation to the background of stars can be observed after a few hours.
For more information about movements and coordinates, see:
Guidance through the Stars! (in portuguese)