Re: turning right...why does it seem harder??
I agree with SupaFly and D-C - When you go to the extremes of control you'll find that left is always easier. Doing a donut to the left is much easier than to the right. The throttle is what gets you.
My lame $0.02 - To cure yourself (as much as you can) practice turning left but treat the handle bar like it is an egg - no more pressure than would break the thing. You need to train your arms to push and pull but not death grip the thing. When your arms are relaxed you'll turn better. You need to apply that same handling technique to your right hand, which gets a tad more difficult. The gas thing. But if you understand the left you should be able to get the smae touch going on the right. I use my thumb and first finger to control the gas - let the rest of the hand to other things. It is easiest to keep the pressure light. Once you do that you should be able to push and pull with your right arm as you do with the left and turning should get eaiser.
Then go to phase two and learn how to use your body. You should be holding onto the bike with your knees and using your stomach muscles to hold your body upright - not your arms. Your amrs should not be carryiing your body's weight. To help this process for those of us with no stomach muscle to speak of, as you turn your outside kneee should be driving down through the center of the bike. Actually push it into the tank and down the enter of the bike. This is not going to turn the bike so much as get your body where it needs to be and doing what is should. It helps you get the lower body doing what it should, which is what it is not doing when you can't turn right. You can't drive your left knee on right turns if your right arm is stiff and your grip is to tight. It also will give you the pecursor to hang off the thing one day.