Typically, I try to check every day, and come up with an idea for a post by the end of the week if I can't post right away. I find that I'm typically on top of things with that system, though things come up from time to time. I also subscribe to every thread that I'm involved in.

I tend to wait a week or so and then send them a message or ping them. Sometimes they just forget and could use a reminder. It's definitely happened to me before. I obviously don't think that it's rude to send them a message via the OOC, but I prefer a pm. I don't care much for pings, but only because you don't really know where it came from until you follow the link. My anxiety just peaks when I see one there for an unknown reason.

I think that the answer to whether you should look for people who respond in a timely manner is a definite yes, though not at first. If you're first roleplaying with someone, just see where it goes first. If you've roleplayed with them before, and you know that they don't respond often at all, then don't bother.

Pacing really depends. Some of the best roleplays that I've been in have slow, but consistently great, while others have been fast-paced and of equal quality. It really depends on the roleplay and the people involved.

You could argue both honestly. Just think back to how many rps didn't get past the first day. Fast replies are fine, but not when the plot stagnates. I believe that it requires a balance to be good.

That depends on who you're playing with. Some people are notorious at dropping out without a word, sometimes before the rp even starts. Personally, I've had some similar experiences with one on ones, so I tend to avoid those. As for the particular issue of people becoming busy in a group rp, why not have them send a quick message telling the other players how their character wants to react and let them work collaboratively to come up with a short little response to get them out of the way until the owner can return? That would help keep the story from stagnating, as well as keep it more fair. No one player can use the owner's absence to their advantage then.