We are just back, didn't do Eurostar so I can't help you there.
Download the app - it will give you the height restrictions and waiting times for all the rides. For a 1 and 3 year old I suspect you will be looking for rides that are less than 1m. There are quite a few.
You will get 2 magic hours (8am to 10am) in the park before it is open to the general public. I suggest using those hours as you will probably get 3 or 4 rides in during that time period. Be warned, only certain rides are open during this time. Discoverland - Buzz Lightyear and oribitron are open, the carousel is open, dumbo is opened, the teacups are open and I think Peter Pan is opened. The queues won't be as long during this time so take advantage. Your kiddies should be able to go on all of those rides with an adult.
Personally, I wouldn't be taking a 3 year old to the dinner with Cinderella as she won't remember it and it is mega bucks. If you want to see princesses, you could queue for the princess pavilion but I have never seen the queue less than an hour. A better approach would be to have a bit of a sit down over beside the small world ride. There is a big massive wooden gate just after it and the princesses and characters all enter the park and leave the park through that gate. If you time it right for before or after the shows you will see them entering and leaving and they will wave and smile. Belle and Cinderella were also over by the Casey jr ride and people weren't aware of it so there were no queues to meet them - something else to keep an eye out for.
That area is really good for smallies as you have Small World, which is still a favourite now that DD is a bit older, Casey Jr, there is a ride beside it on a boat - can't remember the name, cups, maze and dumbo etc.
You can bring food into the park - there is no restriction on it that I am aware of. Bags will be scanned on the way in, but they are looking for weapons, not food, no issue with drinks. The Earl of Sandwich is good for snacks in the Disney village.
There is no restaurant that I would recommend. Slow service, mediocre food. You have to resign yourself to it and just get on with it. Cafe Mickey no longer has characters - be aware of that. I would highly recommend booking somewhere however as the earliest we could get a table the first night was 10pm so we just went to McD's.
You will be absolutely bunched in the evenings, especially with smallies. My DH had an activity tracker app and we walked 28km the first day. People say not to miss the evening show at 10pm but having seen it before and having been up at 7am, we gave it a miss. You will need to be grabbing a space from at least 9pm and entertaining children when tired and cranky and sitting around for an hour, is not fun.
Buy a princess dress here or be prepared to shell out €60 min for one over there. Most little girls spend all day dressed in one.
Also, there is a little shaded playground in advertureland that you might miss.
Breakfasts in the hotels are feeding time at the zoo. Be ready for it.