This should be a basic fact, but I can't seem to find the answer in the owner's manual, or in Google.

In the "maximum data" mode (1 datapoint per second, heart rate, cadence, power), what is the longest continuous ride that I can record with Edge 800, and is there a limit at all, other than the amount of internal storage?

I used to ride with eTrex 30. It had relatively huge internal storage (compared to Edge), ~2 GB, and running out of space simply by recording rides was not a problem. It had a much smaller memory buffer of undisclosed size for the current ride, and it would run out of memory after about 5 hours of continuous recording at 1 point per second. However, data beyond 5 hours wasn't lost, it was simply dumped into internal storage and I could pull it out and stitch with the current ride. (Or I could increase the recording interval to 2-4 seconds, and raise the maximum ride length accordingly.)

Edge 800 seems to have only 100 MB of internal storage and the manual says that it will stick to 1 point/second when it detects the power meter. So I'm wondering what will happen if I go on a really long ride.

This may have improved with the 800, but as a rule, you don't want to let too many rides stack up in your Garmin Edge. Doing so can cause problems with the unit's ability to write a complete file for a ride. When this happens, you have 2 rides that get joined together and have to use third-party apps to split them.