What did the children know about the Radley's family history?

The children know that Mr. Radley only left his house at specified times. and that Boo never left the house at all. As a teenager, Boo fell into the wrong crowd and got into some trouble. Instead of being sent away to school like the other boys, Mr. Radley chose to keep Boo at home. No one had seen him since.

facts about Radley's family history

why did Jem decide to touch the Radley's door

If I recall correctly it was to prove that he wasn't afraid to go near the house instead of being at the fence.