The key is that you don't want to cause over-heating in wire. The answer is you can probably do what you want unless it involves high current and a small cross section in wire mold such that the Romex could generate too much heat. You could always strip out the wires inside the Romex and just run them in the wire mold.
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No, electrical wires can only be run in parallel on wire sizes 1/0 and larger. To supply a load of 30 amps you will need #10 wire and a 30 amp breaker.
If you are talking about #6 building wire, it needs to have mechanical protection. This means that it has to be run in conduit. If you are talking about #6 cable set like Romex, then it only has to have mechanically protection below a five foot elevation from the garage's finished floor. If the wall that the cable set is running in is going to be finished with drywall or plywood then that is considered protected.
What kind of wire? If it's a power wire, why is the place wired with conduit? Commercial buildings must put all power wiring in conduit, so if you're planning to run romex in a commercial building, the answer would be "no", it's not permissible. If it's data wire, note that there may be some "crossover" interference if the data wire follows a power wire for very much distance. It's usually not a problem to cross a conduit and tie to it, but it's generally recommended that you not tie data cable to conduit.
Yes, as long as you do not run it under the floor joists. New electrical code requires that you drill a hole through the floor joists and run the wire through those holes. It cannot be hanging under the floor joists. If you see wires are already running under the floor joists then go ahead and run the wire under the joists attaching it on every other joists with a wire staple. Make sure they wire does not make contact with any metal ductwork or any other metal objects. Match the wire with what is already in the wall outlet you are jumping off of. If it is 12/2 then use 12/2, if it is 14/2 then use 14/2. Never mix wire gauges.
n you run thhn wire in a cable tray