I'm going to offer some general answers, but keep in mind local codes and your AHJ will be the final governing authority.
You can install a genset under deck. But keep in mind general clearances, 3 feet all around for servicing and access, and the exhuast 5 feet away from any building openings, such as doors, windows, dryer vents, makeup air for HVAC, etc. CO poisioning is a real issue, so keep that in mind.
I've seen plenty of installs that violate these clearance rules though... not saying it's right though.
It's advisable to keep the genset within a reasonable proximity to services (minimum 3 feet) but the genset can be installed as far away as you want too. Just keep in mind the further away you install the genset, the greater the material costs will be, not just length-wise, but size-wise as well.
You'll need to run much larger wires, which means larger conduit, and you'll need much larger gas lines. For example, you could run a typical 16KW genset with 20 feet of 3/4" pipe. Move the genset 150 feet away, and now you need 1 1/4" piping. Ditto for the cabling. Then these items need to be reduced back to the sizes the genset allows.
The biggest question is whether you'll be using NG, or LP liquid or gas. You may run into issues with NG if the meter doesn't deliver the required volume for the genset and other gas appliances, as well as the regulated pressure, as many gensets require elevated gas pressure, though newer ones are more forgiving. Volume is still an issue though.
Joe
