1. Parking is $12.00 per day. It will probably cost you less to park instead of taking a taxi. Taxis can be expensive especially if you have several people in your party. It's about 10-15 miles from Disney to Universal. It's really up to you.
2. Both have attractions that are well suited for children. Islands of Adventure has Seuss Landing and Universal Studios has KidZone. There are several attractions in both parks that do not require a certain height. The only requirement is that the child can sit on their own. If you go to
www.universalorlando.com, you can check out all of the height requirements. This also plays into your park tour.
3. All of the information you need regarding the rides and the parks is provided on the main website. The full service restaurants in Islands are Mythos and Confisco's. The full service restaurants in Universal are Lombard's and Finnegan's. There are many quick service restaurants located in both parks. Rain is inevitable in Florida. My biggest tip is to start in Islands of Adventure. All but three of the attractions at Islands are outdoors. The rain is almost always in the afternoon. Another tip with Islands is to go to the right instead of the left. Everyone sees the Hulk coaster and immediately goes there. And by going to the right, you start off in Seuss Landing, which is a great area for small children. Finish your day in Universal. All but Jaws and Fievel's Playland are indoors. So if the rain comes, just get a poncho and go to the indoor attractions. Just because the rain is coming down though, does not mean that the outdoor attractions stop running. When going to Universal, do not let the wait times at Jimmy Neutron and Shrek 4-D deter you. These are the first two attractions inside the park and it's where everyone goes first. A lot of people make the mistake of purchasing Express passes due to the posted wait times at these two attractions. If you go to the right once you enter Universal, you will come up on KidZone which is the other area for children. If you start your day at Universal, beware that KidZone does not open until 10, sometimes 11.
Make sure you grab a park map once you enter the park. This is really important for a few reasons. First, it tells you what the attraction opening times are for the day. So you will know when KidZone opens. The park map also provides you with the show times and meet and greet times. If your child likes Scooby, Dora, or Sponge-Bob, you can take pictures with them. The same goes for Islands of Adventure. Not all of the attractions open at 9. Some do open later in the day.
Hope all of this helped.