1. If there is more than 1 contest going on at a time you have more than 1 ballot. Again this is a simple solution to a dumb problem, you have poorly designed ballots.
If you don't trust the tabulating machines, we have mechanisms to check them at scale. Basically, randomly sample the paper ballots and check them against the machine results. https://en.wikipedia.org/wiki/Risk-limiting_audit
If you don't trust the people running elections, you should know that polling places in the US are run by community volunteers. Literally anyone who's a registered voter can participate and see how the sausage is made. In fact, there's a shortage of these folks, so boards of election are thrilled to get more people participating.