If you have a chronograph, a good way to determine if a heavier pellet is suitable for use in your springer is to try progressively heavier pellets and see where energy peaks and try to stay around that approximate weight. My Beeman RS2 (previous model to yours) in .177 cal produces 13.3fpe with 7.3gr, 15.1fpe with 8.3gr, and 15.8fpe with 10.3gr. I have yet to try anything heavier but it shoots the JSB 10.3gr exceptionally well for a cheap springer--1/2" groups on average at 25 yards and dime-sized groups at 43 yards if I really concentrate--so I stick with those.
There is a screw on the front of the trigger that adjusts the length of the first stage. You will need to take the trigger guard off to get to it. Good luck, and I hope you enjoy the gun.
Groups should be measured center to center. You actually measure to the most distant edges of the group and then subtract the diameter of the projectile to get the center to center size. Since you have a springer, you need to be careful about how you hold it to shoot accurately. Most springers are hold sensitive and won't shoot very accurately unless held loosely so they can move as they want and held the same way for each shot. Google the "Artillery Hold" and try it with your gun. Also note that many guns need lots of pellets down the barrel before they settle down, and many guns are pellet sensitive. There are trial packs of pellets available from various sources so you can try a variety of pellets to see what your gun likes best.Let us know how things go.