Are gate ramps sloped?
(Source) Drain system.

ICAO SARPs Annex 14 does not mention a direction of slope, it only says:


  Recommendation.— On an aircraft stand the maximum slope should not exceed 1 per cent.


So that's fairly level. But tiny slopes are needed, but not necessarily facing away from the terminal. They are needed to guide the rain (and any fuel) toward the trench drain system.

Not always are the drains parallel to the terminal and behind the parked aircraft. They can be parallel to the plane's longitudinal axis or even at the terminal.

I have never seen a parking that intentionally overshoots the mark. What you may have seen is a small backward jerk, like when trains stop. That's due to the offloading of the nose landing gear.

Pilots are guided in via stand guidance systems or ground marshallers. And they stop when the stop sign is shown. Guidance systems are never calibrated to overshoot the spot (the pilot might end up having to blame the birds).