Usually you can't take the formula water unless it's already mixed with the formula. You'll have to buy a bottle of water in the terminal. A car seat is never easy to install on a plane. If it's rear-facing it's impossible. I would look into the CARES harness if your kid is big enough for it. Yes you can gate check a stroller. Just make sure if you need it in transit to ask for it back on the jet bridge at the transit point and not at baggage claim at your final destination. Upgrading 3 people is damn near impossible.