Furnace Vent Rating Requirements

Is there a maximum distance single wall vent can extend before it connects to dual wall/b-rated pipe?
Is the dual wall required to run all the way through roof?
If any portion of the vent is transite is this a safety issue? Why?

The shorter the distance of the appliance to the vent the better, putting a furnace or water heater many feet away from the chimney is a problem, other wise so long as the single wall connector rises and has no dips, and is at least 6 inches from combustible it should be OK. Visualize what happens to a horizontal connector as you move the furnace away from the chimney. Vertical rise distance for a connector should not be a problem if the furnace and chimney are in the same space heated space.
Yes double wall is needed through floors and the roof for more than one reason, firestops are needed at each floor penetration.
Transite has asbestos, so the usual narrative for asbestos, otherwise it is OK, I believe clearance from combustible requirement is the same for transite as for single wall pipe.

I’ve heard that transite pipe is usually cooler than the metal piping and where these two connect it is common for the products of combustion to be pushed back down and escape at this connection. Confirm?

I have never worked with transite pipe, and have only seen it once, but if it is considered the same as single wall pipe than all that applies to single pipe applies to transite. Single wall pipe vent should not be used in an unheated space because of the back drafting issue.