Four strokes carry their oil in crankcase instead of in the fuel like a two stroke, if you lay them down then oil could get into the cylinders causing a hydrolock condition and oil getting into the water.
As for carrying it, depends on a few factors. How long is your bed? What type hitch are you considering?
I've got a short bed truck and I'm carrying an EX4500 generator that is considerably taller than the bed and extends back a couple of feet. In general, it's not been an issue. However, I can't do a 90* turn anymore.
If you built a device that allowed you to stand it up in the center of the bed up front then you could get away with most of your turning radius.
Now-2014 Sierra 346RETS 5er BUB
Then-2002 Keystone Springdale 286RLDS TT
Nights camped in 2014-28, 2015-127, 2016-10