I doubt the base will fit, unless you are flying first class. You don't need it, the SR installs great with just the lapbelt on the carrier itself. If you want the base for your destination, pack it with your checked luggage.
Yes, the SR should fit fine. check
www.seatguru.com for more info.
Sometimes FAs will help you with your stuff, sometimes not. Depends on the airline, the crew and the alignment of the planets. Try to pre-board, though some airlines no longer allow this (Bah, Southwest).
Some airports will allow someone without a ticket to accompany you to the gate, others do not. However, a SR is pretty easy to travel with. Take a stroller it fits into (gate check the stroller), use a backpack for your carry on. Take a sling/soft carrier of some sort too, if that works for your baby. The stroller and carseat (and all the usual other stuff) has to go through the x-ray machine at security. If they won't fit, they have to be hand-scanned, which sucks. If baby is in a sling, some TSA people make you take them out, others do not.
If you bought a ticket for baby :thumbsup:, they get their own luggage and carryon allowance. However, if you are flying alone, I HIGHLY recommend only taking one carry on. Pack as many diapers as you can, an extra change of clothing for you and two extra changes for baby. Couple of receiving blankets, lots of gallon ziplock bags for any accidents.
ETA -- I need more coffee -- I missed that you have 2 kiddos. The intera should fit fine, again check seatguru and your airline. Do you have a double stroller? Bring that, bungee the Intera to it through the airport. Or, if you want to only bring a single stroller, get a Gogo kids set of wheels for the Intera. Leave lots of time through security b/c you'll likely have to have the double hand-checked.
You *might* get grief from the FAs for having 2 children side by side if you are in a 3-seat configuration. Technically, they can give you grief for that -- the FAA recommends child seats only on the window, but AFAIK, the regs don't say you can't put 2 child restraints next to each other in the same row (ie., one on the window, one middle, parent on aisle). If you are in a 2 seat configuration, you'll have a problem b/c if the plane is full, you'll have you and one child in 2 seats, then a stranger and your other child on the other window seat. Obviously, this isn't ideal, but they won't allow you to put the child on the aisle if the window seat is occupied. If you're in a 2 seat configuration, I'd be inclined to put the baby by themselves and you sit with the older child, as the older child will need more of your attention -- hopefully the baby will just sleep the whole flight!
GL!