re: How many days in the future do extended forecasts become useless?

Depends on where. Some places are easier to forecast and models agree more frequently and further ahead than they do for other places.

In general though, beyond 2-3 days is a good general rule to consider a forecast not very reliable. For up here in the mountains, beyond 2 days isn't worth planning around. For Houston, 3 days out is usually somewhat reliable in a general sense. No matter where though, if timing and amount of precipitation is what you need, the day before is best of course.

ETA: NWS re-runs models and updates their forecasts multiple times a day, I think every 6 or 8 hrs if I remember right.