“Can Trump issue an executive order making it illegal to send out ballot application forms...”
Elections are pretty much state matters. I’m sure the Feds can step in if a state tries to disenfranchise voters, but deciding to vote by mail is up to the state. It is also up to the state to investigate voter fraud. If you are in a dem state, it won’t be looked at. If you are in a Republican state, the state will be accused of racism if it looks too closely.