Rating question

Is the rating system sensitive to what level is your opponent is?
ie Does it reflect if you beat someone rated much higher than you?
To what degree?

Yes
Winning against a higher rated opponent will give you more rating points, winning against lower rated will give you less points.
If the gap is high enough you wont lose/gain any rating

> If the gap is high enough you wont lose/gain any rating

you will always lose/gain rating, it will just be less than 1 point, and that will be displayed rounded to zero. ratings are stored and calculated to a higher precision though than shown in games.