Which ones are correct and why?
1-Everyone should have a bed in their house.
2-Everyone should have a bed in their houses.
3-It's up to everyone's personal choice.
4-It's up to everyone's personal choices.
Everyone is a pronoun that means "each/every person." When you use it, you are talking about each individual within a group.
You might then see why the following are correct if you view the phrases as (unnaturally) more explicit about the individuals:
Each one person should have a bed in their house.
It's up to each one person's personal choice.
That being said, the following would be valid if every person has multiple choices that they make:
It's up to everyone's personal choices.