With most things in the U.S., that apparently comes down to how the specific states handle it. Like that already starts with the fact that some states prefer mail-in ballots, some allow it without an explanation, while others require an excuse not to vote at a polling place. Here's a map.
- If I receive a mail-in ballot, and sign my neighbor's name on it, and mail it back, what will happen? (Assume I successfully forge my neighbor's signature – it looks exactly like his). Also assume my neighbor voted too — is the vote counted once, twice, or not at all?
According to Wikipedia:
The election office prints a unique barcode on the return envelope provided for each ballot, so processing of each envelope can be tracked, sometimes publicly
So not only would that likely invalidate your own vote and not work with regards to spoiling your neighbor's vote, because the return envelopes are personalized, but you'd also likely face legal trouble for impersonation, identity theft, forgery, or all of the above.
- If I and my roommate receive ballots, and I sign mine then offer to sign hers in exchange for doing a chore, like the dishes, and she agrees, is there any way to prevent that? (I assume not, but just curious, since it seems this would go completely undetected).
What do you want to sign here? Like again not an expert and that may vary by states, but afaik your ballot is supposed to be secret, so you're not supposed to sign that anywhere (again check the instructions for your state). So most likely you'd sign the envelope or a statement within the envelope that that is your vote. So are you doing chores for one signature? Now I guess an "X" for a person is hardly distinguishable and that's kind of the point (secrecy), while your signature or in that case that of your roommate can be checked against other versions of your signature that you might have provided or had to provide starting the process of receiving your ballot.
Not really the 21st century method and could cut both ways in that sloppy handwriting could be exploited to dismiss a valid signature, while sloppy checking could be used to green-light an invalid one, but yeah that layer of fraud protection is apparently in place. So (depending on state and whatnot) criminal charges for chores and not doing one signature doesn't seem worth it.
- If I work for a political campaign in my neighborhood, may I walk around the town and knock on doors, reminding people to fill out their ballots. Assume they voluntarily fill it out, but I may stand and watch them as they do it.
Apparently apart from the vicinity of the polling place reminding people to vote seem to be legal in the U.S. Watching them fill out their ballot is likely illegal, though probably hard to prove. Though the more often you do that the more likely the witness accounts will pile up and get you in legal trouble, while if you're doing it scarcely, the effect will be negligible for the potential crime...
- Same as above, but the person says they do not have a ballot – may I give them one (that I received from the state legally, if such a thing exists) and then they fill that out?
Where would the ballot come from that you'd give them? Like, you're not supposed to have more than one in the first place. Also, why not just direct them to the authorities? Usually there are methods in place to either exchange a damaged ballot for a new one, to invalidate the old one in favor of a new one (for example the barcode envelope number that refers to you could be changed in the registry invalidating the old one), and so on.
But even if you report yours missing, receive a new one and later find it again, so that you have two, where would you want to cast them (if it wouldn't already be invalid)? Like I'd assume there is some registry that checks if you're eligible and if you have voted already (no matter the method or the place), so if you stuff two votes in one envelope that is immediately invalid and likely criminal. The polling places are also likely to be watched and giving the ballot to an ineligible voter would cause the same problems just for a different person.
- I steal my neighbor's mail and fill out his ballot and send it back. He then votes in person. What happens? Assume that I forge signature successfully.
There are so many things wrong with that. First of all, in order for your neighbor to receive his postal voting stuff, that would either be a place with all-mail voting, or they'd have needed to request that and would thus be checking their mail and potentially complain that it isn't there yet. Also (depending on the state) they would either vote with the ballot received in the mail or need to exchange it at the institutions to be able to vote in person. So the in-person voting should fail as they are not eligible upon which the registry could be checked, whether the mail-in-ballot is already or still present and un-opened, the signature could be checked and depending on where in the process that became apparent this could all be reversed and he could get a new ballot, while the mail-in-ballot would be destroyed or kept as evidence for a fraud case.
So that would again be a lot of ifs and a high risk of criminal cases, for a rather low chance of successfully casting 1 additional vote.