We're going on a trip in two weeks when DS will be 5 months old. We are bringing his Peg Perego infant car seat. He is traveling as a lap infant, but we can use it onboard if the flight isn't full. If we don't bring it onboard, we will check it at the gate.

My original plan was to bring our UB Vista with the seat and gate-check it (in the UB travel bag). DS has only been in the stroller seat once, so my plan was to get him used to it in the next two weeks. The reasons I want to use the stroller seat (as opposed to snapping in the Peg Perego) are:
1) We'll be outside for several hours, and I want to use the Vista sun shade.
2) We have the option to forward face.
3) When it's warm, he'll probably be more comfortable in the stroller seat than in the padded car seat.

So my questions are:
1) If we check the car seat, should we use a car seat bag/cover?
2) If we bring the car seat onboard, do I still try to nurse him during take off and landing?
3) Should we bring the Vista stroller seat or leave it at home? What would you do?

Thanks!