Re: flying with a 3mo old?
A small infant carseat (like a graco snugride) fits in the overhead compartment so you can bring it on board and stuff it overhead as a carryon. Not sure about a graco 35 which is a little bigger, but the 20lb infant seat fits (on TAM and Continental/United).
One flight (TAM airlines) we had the carseat with us in the seat, and DS was in it asleep. We were told by the flight attendant that it was against airline policy to have a child in a carseat during takeoff and landing and that we had to hold him. Which was awful because he was already asleep and cranky after I woke him up.
On a long flight, try to get in the front - there is a bassinet where you can put the baby down if they fall asleep.
We have a graco carseat and stroller frame. Last time we gatechecked the carseat and frame as two separate pieces and picked them up at the gate on the other end. We also bring the ergo with us. Sometimes DS will wake up cranky so we put him in the ergo and walk up and down the aisles of the plane as long as there is no turbulence.
If you want to rent a carseat, double check with the rental car company.
Most hotels I've stayed at in the US provided a crib.
I've been on 4 flights (round trip - 8 if you count each individual flight) with DS, who is 8.5 months old. The white noise of the airplane is great - he sleeps really well most of the time. We only had a few instances when he didn't.
I breastfeed at takeoff and landing to help his ears, and I bring a cover since airplanes squeeze people close together and there is less privacy (normally I breastfeed in public no problem but when there are strangers sitting really close either side of you and staring it gets a little uncomfortable.)
And yes I think you need to take the baby out of the carrier to go through security. And if they need to search you, you aren't allowed to put the baby down, or hand the baby over to your husband. I had braces on my wrists and could barely hold my son when my necklace set off the metal detector and I had to stand still holding him which was extremely painful. They got really mad when I asked if I could give my baby to my husband to hold while they searched me.
DS born 8-15-2011!