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" 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" 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" of radial separation, which isn't sufficient to keep that from happening.)