---If you've ridden with Precip or similar items with hoods, is the hood useful while riding, either under or over your helmet, or is it just something you'd put up when off the bike?
You can wear the hood either over or under your helmet, but it's very important that the hood doesn't obstruct your vision whereever you wear it. Personally, I've never owned a hood that met that requirement. Also, you tend to get sweaty when wearing a rain coat, and wearing a hood leaves no place for the heat and moisture to leave via your neck. Never the less, a hood is handy when you are off the bike and not wearing your helmet. I use a detachable one and carry it in my raincoat pocket. Or try a "Seattle Sombrero" for off bike use. It also is a good sun hat, keeps your head warm on a cold day, and there's a cord to hold it on when the wind blows. Try a search, or, REI has them. Unfortunately, they aren't cheap.
While I'm riding, I use a helmet cover. Cheap helmet covers come free along with some hotel/motel rooms. It's called a shower cap. Handle gently as they tear easily. Also, they may not fit a large helmet. In addition to cheap shower caps, there are also some plastic bowl covers from the grocery store that may work. Or, you can buy a helmet cover made of GoreTex or similar material. (Adventure Cycling sells some.) Having it made of a material that breathes helps, but the perfect raincoat/helmet cover material has not yet been invented. Another advantage of a cheap helmet cover is that you can use it to protect your bicycle seat from dew and rain during the night if it's parked outside, or even if you stop riding and run inside during a downpour.
---If you've ridden with gear with a butt flap, how handy is that?
It definitely helps to have a raincoat/flap long enough to cover your back so that the water drains to the ground rather than down your shorts. If you don't use fenders, or aren't carrying gear on your rear rack, you'll get a nice muddy stripe down your back. If the flap is too long, it may end up between you and your seat causing your seat to get wet. Also, if it's too long it may catch on your saddle as you get up and move forward, a rather embarrasing way to crash.
---Will you ride longer in the rain before putting on rain pants because of it?
Yes, rain pants are a nuisance. They tend to get all sweaty inside. They stick to your legs and make pedaling harder, or they flop in the wind if baggy. However, they can help keep you warm (if not exactly dry) on a cold, wet, windy day.