1. Besides highsticking and cross-checking, what are the common penalties?
Interference (away from the puck, impeding a player by with a leg or a shoulder)
Tripping (stick hooks the skates/ankles and player falls to the ice)
Too many men on the ice (maybe during a shift change, player leaving the ice impedes another player or is inadvertently involved in a play)
A Minor penalty is 2 minutes. Some minor penalties causing blood go to a major penalty. it is 5 minutes for a major penalty and with a major penalty, the penalty is not over when a goal is scored (unlike a minor)
2. What is an icing?
A player on his own half of the ice (red line is the rink's middle line) sends the puck untouched all the way past the opposite team's goal line (the line that goes from side to side along the edge of a team's goal). Essentially they have sent it to the end of the ice (or just about). However if his own team touches it first it is not icing. Also, refs will call off icing for various reasons. Note, when a team is down a player due to a penalty, that team can "ice" the puck without it being called (to aid in killing the penalty).
3. What are the positions and their roles? I think I know the defenseman is the enforcer type that isn't known for his offense, is this correct? What are the other positions?
(Generally speaking) Defensemen, when their team is in the opposing team's zone play away from the goal/closer to the blueline. Wingers and the center play more to the forward corners/side/front of the goal/ behind the goal. It's a bit more complicated but that and as action happens things can switch up some......but that is the general idea.
Also, teams generally have 4 lines of players with, obviously, the #1 line their best (or theoretically their best). Lines/platers are subistuated as the line/player are tiring/have been out there too long/matchup against another line/better line is ready to come in/strategy. Changing lines is done during stopages (unless not allowed by rule like when you ice the puck) and teams will dump the puck into the opposition's end sometimes just to make a line change (or other things to give the team enough space/time to make a line change). It is believed that the Bruins have a superior #4 line and this has been helping their playoff success.
5. How is Jaromir Jagr still playing at a high level?
Some would argue he isn't. Ray Bourque was another guy who played until a ripe age. Conditioning, heart, genetics/injuries weren't too numerous is the likely reasons some guys can play until/after 40.
6. Why is Crosby so soft?
He suffers from being a punk
For stats, some numbers that have importance: Penalty minutes/power play opportunities. The number of goals scored on the Power Play compared to the total number of power play opportunities. The number of Power Plays killed compared to how many goals you allowed the other team to score on their power play opportunities. Number of face offs won compared to the total number of faceoffs (something the Bruins have been good at). +/- (for the total time a player was on the ice, how many goals did his team score minus how many were scored against his team. Obviously a negative number is bad).
Hockey is often about that individual battle. The ability to wrestle the puck away and/or simply create space from the defender(s) which allows the chance for a unmolested shot or for teammates to setup for a scoring chance and you can feed/pass them the puck. Crisp passing so that the receiver of the pass can receive in stride or shoot as a one timer is obviously important tpp. Punishing hits to make the other team just plain suffer and throw them off their game. Trying to keep the offensive pressure up by keeping it in their zone and keep the scoring chance possibilities alive. Blocking shots before they even reach the goal
You probably know some of this stuff already but I figure I would help as much as I can. I hope it helped.....