You've got a good start with the sit and stand stroller. That will be key. I always encourage my daughter to ride even though she's old enough to walk, because she gets really ambitious, and it saves her legs and keeps her from getting too overtired too quickly later in the day.
First of all yes, you can take your stroller on all of those things you mentioned, but you'll have to collapse it on the train and bus and trams (not sure about the monorail- sorry). We hate taking all our carefully packed stuff out of the stroller, so we usually walk and avoid trams etc (and have timed it and found we can get places faster that way- no lines, just good exercise!). When you want to ride something, send one parent in and you can get a "rider switch" pass which allows the other riders in your party to go on without waiting in line. It's good for two other adults. Very fun perk of being a parent. And by the way you can always park your stroller, there are tons of stroller parking spots everywhere.
Some of the rides have fastpass. Figure out which ones you want, and as soon as you get there, send an adult in your party over to those rides with your tickets. Because of the rider switch, you can get more than one fast pass at a time. That way you are guaranteed at least two, perhaps three rides with practically zero lines for everyone all day. Then the other lines won't be so bad. Other people will probably have specific tips on the best times of day to ride which rides, but we always like to ride the long-line rides when the parades are going on. You'll get a system down pretty quickly on your first or second day there.
We usually get there, ride one or two rides, then go for an early lunch. Then we ride a bunch right after lunch while everyone is filled up on food and relatively docile.
If you have nappers, you'll want to bring a large blanket or neatsheet kinda thing to cover the stroller; even if you can find a quiet place, it can still be noisy and chaotic!
For babies, there are the baby care centers. These places are like a baby oasis. Find it on your maps and circle because you'll be going back often! They have nursing chairs, high chairs for feeding your baby, changing stations, they even sell formula and diapers and wipes. And staffed by very helpful ladies. We went when my son was 3 months and went to the baby care center three or four times that day. So I predict for a week you will get to know the baby care center pretty well.
Hotels...we are local, but when we have stayed there we like to stay at the property closest to the park with the best pool we can afford. Hot tubs are nice for those sore muscles, too. :D It does make a difference, the days can be exhausting. Everyone thinks they'll go back to the hotel room for downtime during the day, but logistically this isn't as easy as you'd think. Distances are far and it's not so easy to pick up and go all the way back even if you are on-property. That said, if I could splurge, I'd stay on-property in a heartbeat.
Have a really great trip! Disney is so much fun.