In guided mode, when I tell my airplane (via Mavproxy) to fly to a point it that is much higher or lower than the current altitude, it changes height very slowly (never exceeding a pitch angle of roughly 10 degrees).
What parameters should I change to enabled my airplane to climb and decent at higher rates ?
This is the normal behavior, that the sink rate is set so that the target altitude is reached at the target point. Anything else would be bad airmanship unless you have a special reason to do so.
My goal is to maximine the capability of the airplane to not miss waypoints in cases when they’re close to each other on a 2d map but have a high elevation difference.
What TECS parameters should i change in order to achieve that ?
TECS tuning is a full system. Go through the link above and work your way through the process. TECS tuning takes a while but if done right it will maximize what your plane can do.