S.G.
I have two kids who I breastfed; to answer your questions:
1) The two breasts are probably just different. I think if you continue to switch sides (pin a safety pin on the side of your bra that the baby will start the nursing session on and switch the pin after each session) it'll even out. I usually put the baby on "side 1" for about 20-30 minutes, then switched it up to "side 2" when "side 1" seemed drained.
2) springing a leak is 100% normal; the first time my husband and I were "intimate" after baby #1 was born it was like a pair of milk-filled fire hoses were at loose in the bedroom!
3) my babies did this when they kind of lost their way on the breast. They were trying to find their way to a comfortable nursing position and a good latch. You could try a couple different holds with the baby to see which works, and do you have a nursing pillow? My Boppy helped the baby be at exactly the right spot for effective latching.
Relax! And enjoy this time together with your new baby.