I'll help on 2 and 3
2. That is one poor thing about passing. Its not quick enough in certain situations. When you're going to the corner or the boards and you need to move the puck ASAP, its best to ditch R2 as a mechanism. Hold R1 and use your right stick to slap/chop at the puck. OR if you have enough time to actually gain control, immediately use your right stick to throw the puck around the boards or to another teammate by directing with the left stick. You'd be amazed how well this works as far as moving the puck quickly. It can give you some great odd man chances too.
You might take some icings but the better you get with directing the puck off the boards or too a teammate, the more success you'll have.
Both the stick chop and right stick passing take getting used to but once you've got the discipline down its a great tool and can really help you win hockey games.
3. This is a simpler answer. Use triangle. I really would like board play to be enhanced next year because its such a fundamental part of hockey. But in the meantime, triangle is the tool, and it is massively underutilized. When you're going to the boards to chase down an opponent with/getting the puck, hold triangle and pin him to the boards and let your AI/teammates come in a clean up.
Hope these help.