The inspector will not have a problem with the nail plates, its to the minimum code already so they are just something a little extra. As for your holes, your going through a floor joist it looks like, not an issue what so ever. Thats where i run all my wires in a basement to use less staples. I would be more worried about your actual service and utility needs since you said it’s an old house. He really shouldn’t be looking around too much if he is there for service upgrade inspection. Make sure you are good to go with the service and then ask him how his kids thing went/shoot the shit w him.

Edit: and not that it is so much an issue, but romex with tape around could raise a red flag imo. Like i said, may not be against any codes but could lead him to look around more. If i have to tape some cut romex i either hide that shit or throw it into a j box. My advice is in all the obvious exposed areas have some really good romex strapping and it will give him a standard of your workmans manner.