The best time of the day is whenever you can go
Those are the real thing, and there are variations of them that have the same conical shape, hollow stem, and pits -- but different colors -- black, gray, yellow. Another type called a half-free morel that has similar pitting, but the cap doesn't come down as far and isn't connected to the stem at the bottom -- they're sposta be pretty good though I've never had any. The false morels, or reds, look very different. Some folks eat them, but there's plenty of folks that get pretty sick from them. I don't know why anyone would take the chance. MDC has a pretty good primer on mushrooms here.
I like to simply saute them in an oil/butter mixture with salt and pepper. Once they're done, drop a little more butter in the pan to melt, then pour the the whole thing over a good piece of toasted bread. They are excellent breaded and fried too. In my opinion, simpler is better. I see some recipes that have so much other stuff going on that the morel is lost. They're too delicious and rare to do that to them.