Is it best to remove existing tiles or tile over?

you can tile over tile. but if its a smooth tile thats already on the the wall, it will need preparing. you could either score the tiles with a angle grinder, whitch is time consuming, and can be dusty. or you can aply like a grip paint over the tiles. this will give the adhesive somthing to grip to, and give a better bond. im not sure what this stuff is called but its like a paint with fine grane mix.

Yes you can tile over tiles, it does not matter if it is a glazed tile,but you should really remove the tiles as you do not know how well they are fixed,but if this is not an option and the tiles feel sound then tile over them,you do not need to prime them as long as they are dirt and grease free,but if you do want to prime them I would use Mapei eco prim grip this is expensive but a really good product.

all depends on the tiler ,personally I would knock them off, you can over tile on small splash backs on kitchens . But if you were fixing likes of travertine in a bathroom I would be pulling the old tiles off, you have to think of the extra weight you will be putting on the walls, its a messy job taking them off but I think it's the best way for a proper job