I am wondering how Imperial Edition content works.

1. How many characters may use the horse? Only one or the whole account?

2. Same question applied to all other content. How many characters any faction, How many characters get a mudcrab, etc?

If these bonuses are each for one character only, are they locked to that character or can they be given to other characters on my account?

I would think the whole account. Er, every character.

All of the characters can use them.

all of the characters can use them but you only get 1 set per account

The usual way this is done is that every character created on the account will get one set of the items and they will be character bound.

So if you roll up a new character they will have a horse and a mudcrab pet and the other goodies you spent extra money for.

I can confirm for the horse at least that every character has it available AFAIK no way to transfer it (not an inventory item). You don't get it in the mail; rather, you have to buy it at a stable, but at a special low price. Probably the rest of the stuff is also account-wide, but can't confirm.

https://help.elderscrollsonline.com/app/answers/detail/a_id/5208/kw/imperial%20horse That's the official word.