Why does the Nikon P310 disable flash at infinity focus, and can it be overridden?

I can guess about question 1. You say this is a point and shoot, so it is dumbed down for the masses. Past some distance, the built in flash won't do anything but run down the battery. There won't be enough light from the flash hitting the subject. Light intensity falls off with the square of the distance from the source. Another way to think of that is that the flash looses 2 f-stops every time the distance is doubled. Eventually, and that's probably only a few 10s of feet at best, the flash no longer does anything useful. Because this camera is aimed at people who don't understand all that, Nikon probably figured disabling the flash at far focus distances would keep people from complaining about excessive battery drain, or complaining that their flash shots didn't work. Sounds like a reasonable feature to me given the intended market.

It always amazes me when I see people using flash just because the light is low even when the subject is far. For example, consider how often you see a flash go off in the stands at sporting events. There is no way any of those flashes in the stands are going to add measurable illumination to anything on the field. Just last week I saw people taking pictures of fireworks with flash on. Not only are they too far away, they are self-lit and illuminating them externally would only make the picture worse. There is a reason fireworks displays are after dark.