Besides, should you gloss coving?
Since coving is generally plaster (or plaster look-alike), I personally think it looks much better white as this is the plasteriest colour, and this should definitely be the mattest finish you can find! However, as mentioned above, it can look ok in other colours if thought through carefully - but, please, not gloss!
Similarly, does coving need painting? For example some coving & cornice materials such as polystyrene are very absorbent, so will need several coats of paint to get a nice finish. Other materials such as paper coated plaster coving will typically require less paint but will usually need to be pre-primed first.
In respect to this, should you paint coving or walls first?
the easy way is to paint the coving first, paint the coving and hit the wall , and then when dry cut in from the wall to the edge of the coving. USE A GOOD BRUSH, not el cheapo. If you are using waterbased paint you will need a synthetic paint brush.
Do you paint coving same Colour as ceiling?
If you have a room with a low ceiling, then painting in the coving the same as the wall colour, rather than have it painted in the same colour as the ceiling, will add height to the space as the coving becomes parts of the walls and is not sectioned off as part of the ceiling.