1- Not some randomly, but 100% of them are run through multiple tests before Election Day. To include full on Election Day simulations where the clocks are set and everything is identical and the votes are cast all day long then the totals compared to what they know they cast.

2- Yes. After every election before results are certified the state board of elections makes every county to an audit of multiple randomly selected races and precincts comparing paper records to electronic totals. The precincts and races to be audited are not selected until after Election Day so nobody can work around that if trying to hide fraud.

3- Absolutely for every state on every level. There are poll and election observers from both parties in every county board of elections watching every step. They are writing down every total and you can be damm sure they are doing the basic stuff like making sure the math is right and what they see on their level is what is reported at the state level.