Is URD #4 Appropriate for 100ft run for generator hookup?
Running all the wires in the conduit is fine, but there are better choices than that URD cable!
Bumping up to 2&quot; Schedule 80 and putting all the wires inside it is more than fine (there is an 80% ampacity derate because of this, but it won't bother you one bit here); however, that 4/4/4/4 URD cable is probably not going to be the easiest thing to pull through the conduit.  Using individual 4AWG Al XHHW-2s for the generator feed instead would be a better choice, and you can also save fill by running a 10AWG bare copper ground wire that's shared between the generator feed and the shed circuit.  The remaining wires for the shed can be 10AWG copper THHN/THWN-2s -- this will make your conduit-pulling job quite a bit easier than trying to stuff cables down your conduit.
TORQUE LUGS TO SPEC (so you don't come off looking like a loose lugnut)
In addition, that URD cable uses AA-1350 aluminum conductors -- while legal for URD cables, it would mean that you would have to take extra care to make a perfect termination on your lugs at each end.  Getting individual aluminum XHHW-2s instead would mean you are getting AA-8000 series alloy conductors, which are somewhat more forgiving than the old AA-1350 stuff.  Even with AA-8000 series conductors, though, it's still highly recommended (and even required if your AHJ is up to speed with the 2017 NEC, see 110.14(D) for details) to use a torque tool to torque the lug setscrews to the manufacturer's specified torque values.  Considering that a mistorqued lug can lose you your house, not just a race, an inch-pound torque wrench, applied correctly, is cheap insurance, no?
Temperature ratings matter!
Last but not least on the electrical front, in order to use 4 AWG aluminum cable for this run, you'll need to pigtail it to some copper (10AWG is fine, given that you can change the pigtails out if you get a bigger generator and inlet) at the inlet end, presuming that you're putting a NEMA L14-30 inlet in, that is.  This is because most inlets that size a) can't accept 4AWG aluminum wire and b) are only rated to a 60°C termination, not a 75°C one, which won't limit you at 30A, but would keep you from using the full 60A of your wire should you get a bigger generator and inlet.  You'll need to use set-screw type splice blocks (rated Al7Cu/Al9Cu) to connect the pigtails, not wirenuts, by the way -- don't forget that these need to be torqued to spec, too!
As to that gas line...
Co-trenching of dry utilities (electric/gas) is not an uncommon practice, although it does carry some risk of gas migration into the conduit system for a conduit run in case of a buried gas leak.  You'll need a yellow-insulated, direct burial rated, single conductor (minimum size 18AWG) laid atop the gas line in the trench with a stubbed-up termination at one end to meet IFGC 404.17.3 tracer wire requirements for the gas run, by the way.
If you do wish to run the gas line in a separate trench, I would recommend a minimum of 36&quot; separation between the trenches, so that it's an effective barrier against digging both up in one go with an excavator.  (The NESC specifies 12&quot; of radial separation, which isn't sufficient to keep that from happening.)