1. The requirements are the same as for the “throught the ceiling” installation:
2. “Inverted P trap for heat in the vent circuit, as hot air won't want to go down to escape as easily”. I’m not sure if I understand you correctly… would that be by going up from the register above the shower – horizontal section - and down to the floor level / under the floor where you hook it up to the exhaust fan? If so, you might have some issues with condensation running into the fan enclosure. You could install some kind of an in-line condensation trap to discharge it before reaching the fan box… I’m not sure because I don’t know how you are planning to position the fan and what kind of a fan design is it.
The final horizontal section of the pipe should have a 1/8” per inch slope towards the outside allowing any condensation that may form in that line to flow outside the house. You should also support it every 4’ to prevent any sagging.
3. I don’t see any issue with using ABS or PVC pipe, unlike the “dryer vent” building code requirements bathroom vent discharge pipe materials are not listed. Just make sure you cement all the joints with proper adhesive.
I don’t know the exhaust fan size you’re going to install but I believe at around 200cfm’s they require 6” diameter discharge pipe.
I hope this helps a little, please let me know if you have any other questions.