I would try to get the child un-used to having warm bottles and food, if you can. It's much easier if you can get them to eat/drink at room temperature. You might be able to get the wait staff at a restaurant to bring you some warm water or pop the food in the microwave, but it won't be a priority for them.
Kilian's Irish Pub in Frauenplatz (just off
Marienplatz) is now non-smoking in the back room and they have a high chair. Enough room to park the stroller at the top of the stairs before descending to the pub, too. Might be a good option for a lunch or midday warm-up as a break from the Christmas market at Marienplatz. I have known people to change their child's diapers on a bench seat in Kilian's, too. The view for the other patrons is blocked by the table. Obviously you would be using a diaper changing mat for hygienic reasons.
All the
Starbucks are non-smoking and have high chairs and changing tables. If you're at Marienplatz and have a diaper emergency, you can go into the Hugendubel book store, ride the elevators to the top floor, push the stroller into the handicapped rest room (opposite the escalators), and change the child in his/her stroller. The cafe there (World Coffee) is also nice when it's not too crowded, and they have a high chair as well.
Use the elevators in the U-Bahn stations when you can, but inevitably you will have to use the escalators sometimes. Hopefully you don't have a "jogging" (three-wheeled) stroller with a long wheel base front to back; those are difficult on escalators. When going down the escalator, after you get on, pull the stroller back so the back wheels rest against the front of the step above the one they're on. When going up, push the stroller forward and use the front wheels against the front of the step above to steady it. It takes a little practice, which you might want to do without the child in the stroller if it makes you nervous. Also beware to get the stroller as far to the right side as you can, because people will want to get by you on the left. Hold tight to the stroller going down, because people trying to get past you will bump you and/or the stroller in their rush.
When the train comes, keep a lookout that the door you want to enter doesn't already have a stroller there, or at least put your stroller on the opposite side from theirs. You don't want to block other people getting out with their strollers.
A great time to travel is between 4 and 5 PM, when there are extra trains running for rush hour, but not so many people riding yet. It's best to avoid rush hour if you can.