How long should they interact?

We've been keeping our new kitten, Gizmo, in our master bedroom with the litter box and his food/water bowls in the master bath. After his initial vet check and a week long period of adjustment we finally introduced him to our female cat (Neely) and male dog (Sean). The intro. with our dog has gone remarkably well but not so with Neely. I know it will take time and I actually have 2 questions: 1. how long should we be leaving the kitten out with our other pets (supervised, of course), and 2. what is the average length of time it takes for 2 cats to become friends? I realize every situation is unique.

I think the supervised meetings can last as long as you can stand it. They will eventually have to interact long enough to work out dominance, etc., so delaying that doesn't accomplish much.

It can easily take 90 days for it all to get worked out. I've seen it take much longer, with relationships still developing long after 90 days.