Alright, extending the hypothetical slightly, let's assume that the "stand in" train is actually less crowded (i.e. you can do a quick check on your laptop/smartphone and the train you would be boarding is neither full nor in top bucket for the slot in question). What then?
Well most people would not know if the train was in the top bucket or not. About the best that the average Joe might know would be that there were 8 seats left if they had a smart phone to check things.
Regardless of full or not, assuming that a decision wasn't made by someone in CNOC to carry the other train's passengers, then it would be conductor's discreation on whether or not to allow you to board if you ask. If you just board, again it would be up to the conductor to decide whether to accept your ticket or put you off at the very next stop. The conductor could also accept your ticket, but order you to sit in the cafe car because the train is sold out and no seats are available.
(And of course, there's a possible answer to this: If your initial train is over an hour late on the NEC (or any other corridor) and you're at a staffed station, you might be able to get a sympathetic agent to switch your ticket quickly.)
Again, the agent might decide to be nice & helpful, or if CNOC ordered the other train to pick up the pax then the agent would just tell you that.
1) What happens if a train comes in at the "right" time and someone just walks on and boards it? Assume garbled announcements or that folks are out on a platform rather than in a quiet station.
Again, conductor's discretion on what to do with you.
2) Right train, right time, but the train is on the wrong day. We've all heard of the rather infamous Builder/Zephyr "episodes" where the train is hilariously behind schedule. What happens if someone boards the proper train at (or after) their stated departure time, but it was actually the previous day's departure? I'm wondering just because of the trouble actually explaining that to the customer (no, this isn't your train...yes, it really is a day behind schedule, your train won't be here for at least 12 hours). Assuming a burned-out crew and an unstaffed station somewhere in "flyover country", what would be the status of a passenger who boarded the wrong frequency of a given train?
First, at a very small stop there would probably be little chance of someone not being told in advance that this was the train from the day before
Then it would come down to is that train sold out or not. If not, then they'd probably allow pax to board, at least in coach. It would be far more difficult to accept sleeping car passengers, as those cars are often sold out.
Finally, if you did manage to get on despite warnings from the crew that they were NOT accepting tickets for the other train date, then the crew could decide to put you off at the next stop or maybe even drop you off at a RR crossing. They could also once again order you to sit in the cafe car only.
NOTE: All of the above is how things would have been handled pre-eTicketing. But I would assume that eTicketing doesn't change things that much such that things have changed massively.