Do most modern aircraft rely on the GPS for navigation, and to what
extent do they rely on it?

If you mean "do most modern pilots rely on GPS for navigation?", the answer
is probably "yes". Modern aircraft do still come with a variety of
navigational equipment, but everything in the new panels is centered around
GPS.

And is it true that such aircraft's navigation systems use maps
'optimised' for GPS?

Not sure what you mean -- but most GPS' have built-in moving maps that
display your position relative to the "real" world, as depicted on the map.

And finally, if I may, what level of positional accuracy must aircraft
relying on GPS for navigation work with at typical altitudes
(presumably 20,000 to 40,000 ft)? Are we talking tens of metres, or
over a hundred metres?

GPS positioning is accurate to within 10 meters, often less. That's way
more accurate than any aircraft operating in the flight levels needs.
--
Jay Honeck
Iowa City, IA
Pathfinder N56993
www.AlexisParkInn.com
"Your Aviation Destination"