HI,
I have been twice to Disney World with my babies, the first time we went my son was 3 and my baby only 3 months! and this year mi girl was one and a half and my son 4.
You can take your stroller all the way to the entrance of the rides. No need to lock it, there are usually hundreds of strollers, there is always security around and no one will take your things away. The only thing that may happend is that if you cheat and try to put your stroller way in the front when there is an order to leave them the personnel will move it as far from the entrance they can and will take you a little longer to get to it.
There are plenty of rides you can do with babies, as many as you will have time to do in a day.
There are some tips, like find out the rides you want to try and the ones that are the bussiest get a "fast pass" and come back at your stated time.
I will recommend that you visit the Disney Park website and print the maps of the attractions you want to visit, then read about the rides and choose the ones that interest you the most, that way you'll know where to go in advance and no waste time reading the map at the last moment.
Any ride that does not state a height limit will be a ride that allows kids and babies any size and age. Believe me there are enough.
I love Disney, I hope you have a great time there!
Any recommendations you would like I'll be happy to give you, send me a message.