You are correct in that you can have only one open ED application as it is binding. Some schools have an ED2 option in case the ED1 option does not lead to an acceptance, but that’s a more in-depth explanation.
How many EA schools you can apply to depends upon the rules of each college. Some, like Harvard and Stanford, only allow you to apply EA to their college (with some exceptions).
There is no blanket rule; each college sets its own. So there are permutations where you can apply EA to several public and private colleges.
You should only apply ED if you will have no regrets committing to that school beforehand (even if some other school admits you with a full ride), including knowing that the ED school will be affordable.
The bottom line is you need to take the time to read the details of the admission program (ex. ED, EA, SCEA, rolling etc.) you apply under at every college and determine what is an isn’t allowable under those particular college’s plans.