I am installing radiant heat over an existing concrete pad. After looking at the pictures of using "deck mud" to cover the pipe and create a base for tile, some questions arise. What is the minimum thickness of such a bed, and the minimum thickness over the pipe? Is cracking a problem? Is the tile applied directly over the bed, eliminating the need for backer board? Is it necessary to use lathe or anything between the existing pad and the deck mud?

1-1/4" to 1-1/2" would be minimum. 3/4" over the pex pipe is average.
For deck mud over concrete you need a loose modified thinset mix which is troweled on just prior to placing the drypac. You don't need wire lath over concrete.

For thin slab, such as above, gypcrete or slurry concrete is preferred for hydronic heat systems. The thicker a slab is in actual concrete, the more efficient it is. Same with deck mud.

What size area are you doing?

The area I'm doing is 20'x34'. What are the details of the slurry concrete? A wet portland-sand mix, or regular concrete mixed wet? Does the tile go over this with just thin set? Thanks for the help.

One of the most widely used floor specialists is Maxxon. I would contact them directly for any detailed info on gypson or concrete based pours. http://www.maxxon.ca/
They also have US based operations.

I believe they also have a concrete pour thats specialized for hydronic heat.

Sorry I can't tell you what the actual formulas are for concrete slurry mixes. Those are usually closly guarded by the ready mix companies.