Using a bag or not depends on if you are going to monitor the heat level of the beer, and then what you will do when it reaches a certain level.
When the heat level is where you want it, are you going to immediately bottle the beer? If not, you will need to remove the jalapenos to prevent further extraction...which means you need to bag them (or rack the beer off of them, but bagging is simpler).
With the puree, just dump it in but try to minimize splashing/aeration. When I add purees, I attach long tubing to a funnel. The end of the tubing goes beneath the surface of the beer. That way, when I dump in the puree, it doesn't splash all around.