Can judgements go away over time. In court house? On credit report?

A judgement NEVER expires.

Actually a judgment lasts from 7-10 years depending on area, and can usually be renewed at least once. A debt however, never expires.

Entries are supposed to be removed from credit reports after 7 years. Though they can be renewed.

Can judgements go away over time. In court house? On credit report?

If the judgment is satisfied (paid), you no longer owe it.

The rules of a judgement depend on where you live, in general they last 7 to 10 years but are easily renewed for another term. So you can expect them to be valid for 14 to 20 years.
In some areas a third renewal can be done, in others they will have to prove there is a good chance of collection.

So a judgement can often be enforced for well over 20 years, till they find you have a job or money in the bank to get the money