I have illnesses that require me to have to carry snacks, water and an umbrella and/or hat. I have a normal standard size backpack for them. Will I be able to bring it with me on rides and such? Do I need a note from my doctor? I am not disabled.

Some rides you will have to leave the backpack with a ride attendant for safty reasons.

Yes if it is a normal sized backpack there should be no issue on any rides. There definitely wont be an issue bringing it into the park. You'll still be subject to the basic security check.

You can bring your bag on most rides yes. Some people choose to leave them at the platforms and get them when they are done, but most rides, you can just scoot it under your seat or between your legs. I carried a huge bag the whole time for my family and it never left me.

Yes you can