I believe it's:
Open: 4x Sprint
Clubman: 5x Sprint, 1x Long
Prof: 6x Sprint, 2x Long
Elite: 7x Sprint, 3x Long
Masters: 8x Sprint, 4x Long (=every stage)
Additionally you'll encounter more night stages and bad weather in higher difficulties.
Opponents will always "drive" cars from the same class as you (of course). No that it matters, since times are calculated based on ideal times (per class) with difficulty modifiers and randomness added in. The devs explained the process in one of their roadbook blogs.
The stage times of your fastest opponent actually won't change much from Open to Masters. Only the gaps between the places tighten a lot. Being 30 seconds down in Open might still get you 3rd/4th, in Masters you'd probably finish outside the points.