No and yes. It is not possible for two roosters to fertilize the same egg. But you might get some eggs fertilized by one rooster, and some eggs fertilized by the other rooster. You will have no way to know which egg was fertilized by which rooster, unless you separate the chickens or unless you can tell by looking at the chicks after they hatch.
Not a breed, but yes there can be a hybrid of Sebright and EE. It would be called a Sebright/EE mix, or some similar description.
They just need to be safe (from weather and predators), and separated.
That could mean a separate coop, or a cage for one of them, or something of the sort. Wire dog crates are sometimes useful as chicken cages, especially if your coop or run is big enough that you can put the dog crate inside. Putting the EE male in a cage or dog crate would definitely keep him from mating with the Sebright female, as long as he does not escape from it.
Hens can store sperm, so if you want to be sure of which rooster is the father of her chicks, you should keep the hen separate from all other roosters for 3 weeks or so before you start collecting eggs for hatching. Most of that time, it does not matter whether she is with the right rooster, or alone, or in a female-only group. She needs to be with the right rooster for at least a few days before you start collecting eggs to hatch.
