Yes, you can print your boarding passes at the airport, as well as checkin there. No problem doing that at all. If I have bags to check, I usually don't bother checking in from home....I just get to the airport 2 hrs before my flight and checkin when I hand over my bags.
Yes, Jetblue's fares do tend to fluctuate. BUT....while they can go down, they can also go up. They will give you a credit if the fares go down, but you have to stay on top of them and call when the fare goes down. They then cancel your existing reservation and make a new one so you have to be sure they give you back the same seats you originally selected.
Of course, that policy can change at any time.