Yes, you can certainly get hot water in the baby care centers in the theme parks. The baby care centers all have small kitchens with stoves and microwaves for just that purpose. And the wonderful cast members at the centers would be happy to help you with heating water.
If you'd like to take a look at one of the baby care centers, you can click
HERE (look for the video called "Baby Care Centers"). You'll see a shot of the kitchen toward the end of the video. I can't say enough wonderful things about the staff at the baby care centers. They are kind and calm, and help to make the baby care centers a wonderful oasis in the busy theme parks.
As for your stroller ... there are stroller parking areas outside nearly every ride at WDW. Some of these stroller parks are marked with a sign, but most are just a line outside against a wall or fence. You'll see lots of other parked strollers, just leave yours there too. If you have any concerns, just speak with a cast member.