That should absolutely be a new law. They should all be required to pass a background check, a drug test, and a test on the Constitution before they are allowed to run, much less be in office! After they are in office, they should not be allowed to receive money or gifts from anyone for any reason.
No rapist or felon. Overturn Citizens United that allows unlimited dark money to flow freely to election campaigns.
Yes, and unable to (must freeze) all stock trading.
Also multiple psych tests. And all of these tests and checks should be given in a random order to make it harder to fake it.