First of all, the stab doesn't HAVE to lift down persé. As long as the derivative of the lift slope is negative, it's stable and that can well be with an up-lifting tail.

Also there's the downwash from the wing, meaning that the amount of up/down lift of the stab is a function of not only stick position, but down wash angle as well. Fly slower (or pull G's), steeper down wash, more down-lift on the stab, without changing stick position.

Q1. Look at the pressure field. Negative flaps yield higher pressure on the upper surface of the flap, yielding a nose-up moment. You also get lower pressure on the lower surface of the flap, adding nose-up moment.

You can only get zero stab lift at one angle of attack. Realize that the extra lift of the tail is induced drag, proportional to the tail lift coefficient, so assuming 1G, it decreases with the square of speed. Over a whole flight it's optimal to keep induced tail drag low during slow flight and accept a bit of a lifting tail during cruise. Where the optimum is varies per glider, though for flapped ships the variation in tail lift is tiny.

It seems that 50-80% of the CG range is optimal in most modern sailplanes.