What is the ideal temperature during carbonation with priming for an ale?

You are correct when you say the warmer the brews are stored the faster carbonation will complete.

Carbonation is a mini fermentation, so ideally you would want it to complete around the same temperature as you brewed your beer.

Higher temperatures for carbonation can produce or accelerate the production of of flavours in multiple ways, the first that comes to mind is higher temperatures can stress the yeasts, so for an ale yeast anything over 22C and it will produce 'off-flavours', but some of these esters or higher alcohols may be a desired flavour of the style. Secondly, storing warmer will accelerate the formation of aldehydes by the strecker reaction, ie paper flavours, so once you have allowed enough time for carbonation to complete, move the bottle to a nice cool location for longer term storage.

• Too high temperatures can damage the yeasts and prejudice the carbonation?

This would have to be above 38C to harm an ale yeast enough to affect carbonation, at these temps the yeast would be very unhappy and start to die. If it were a lager yeast then anything about 30 could be harmful, and start killing off the yeast.

Ideally for your ale carb up at 15-25C, for 10 days; then store somewhere nice and cool.

Optimal about 18C-20C. But almost any temperature between 5 and 25 will work. If cooler then it takes longer. It is possible to go higher but there may be some more fruity esters produced although not very much... Best keep it at lower temperature range of 15-20C for about two weeks or so.