The monorail comes frequently. The actual duration depends on the time of day - its more frequent in the morning/evening "rush hours" than during mid-day.
To go from the MK to Epcot, you would take the monorail to the TTC and then change to the Epcot monorail. Figure on at least 20 minutes (perhaps more like 30) do get from one park to another.
The length of line/wait is highly dependent on when you are going. Could be no line at all, could be a very big line.
I've never had a problem with the reliability of the monorail.