#1 is the classic symptom of regulator creep. Solving the slow first shots is sometimes as simple as getting the hammer spring tension adjusted properly. Gradually increase the hammer spring tension until the velocity no longer increases, then back it off until the velocity falls to about 97% of that maximum. For example, if the max velocity is ~900fps, reduce the hammer spring tension until the velocity falls to 900 * 0.97 = 873fps. That will put the gun at a state of tune similar to an unregulated PCP operating near the top of its bell curve...meaning a varying pressure will have very little influence on the velocity.
If that doesn't remedy it, you will need to address the creep at its root cause. Creep is caused by surface defects in the regulator's valve seat. That causes the pressure to rise up most of the way but then a small amount of air will continue to weep through the surface imperfections over a period of minutes or hours until it finally rises high enough to totally squish the valve seat together and completely halt the flow of air. So the cure is to dress the valve seat smooth with an abrasive or replace it if that is an option. If it is a simple geometry, you can use fine wet/dry sandpaper to dress it to a smooth finish. If it is a tapered or convex seat, an abrasive compound (paste) can be used to burnish the mating surfaces together and bring them into an intimate fit.
Note, a leaking O-ring in the regulator will NOT cause this symptom. It's all about the valve seat.
#2 may be another symptom of sub-optimal hammer spring tension. A regulator's input regulation characteristics will produce a slightly higher output pressure when the input pressure is high. That makes the valve harder to knock open and can produce a slower velocity (speaking of the gun's main valve this time, not the regulator's valve). As the pressure begins to fall, the hammer can knock open the valve more easily and the velocity will rise. Then finally when the pressure falls low enough, the velocity will begin to drop. The result? A slight bell curve shape.