You can do all of this using weatherproof boxes and conduit especially if you are not opposed to having conduit visible. It will only require a single 3/4" hole through the wall.
Supplies:
1-gang rectangular weatherproof box.
round weatherproof box.
1-gang In-use cover.
3/4" PVC conduit.
3/4" male terminal adapters
3/4" PVC conduit clamps.
Procedure:
Start by boring a 3/4" hole through the wall where you want the conduit to pass through the wall. You can hide the hole by entering the receptacle junction box from the back knockout, so the junction box will cover the hole.
Next you'll want to slide the conduit through the hole, and seal around it using either silicone caulk or Duct Seal. Then using the 3/4" male terminal adapter, connect the conduit to the rectangular junction box. Seal the rest of the knockouts in the box, using the supplied knockout plugs (leave one open to run conduit to the light box).
Seal all but one knockout on the round box using knockout plugs, then mount the box where you want your light. Using a couple more 3/4" male terminal adapters, connect a length of conduit from the rectangular junction box to the round junction box.
Pull the cable, and install the fixtures.
Finish the receptacle installation with an In-Use weatherproof cover, this will allow the box to remain weatherproof even when things are plugged in (I like the low profile models, because they are less noticeable when not in use).
Use the 3/4" PVC conduit clamps to secure the conduit to the wall about every 24-36".
Extra Weatherproofing:
For a little extra weatherproofing, squirt a bit of silicone caulk around the screws used to mount the round junction box before driving them all the way down. Then run a bead of caulk around the top and sides of the rectangular junction box where they touch the house (don't put any on the bottom seam). This will prevent water from getting behind the box, and leaving the bottom unsealed allows any water that might get in to get out.
Safety:
Remember, because the receptacle is in a "wet zone", you'll have to use a GFCI receptacle (or have some other form of GFCI protection for the receptacle).
Sounds like a good idea. You will need to put a layer of roofing felt over the plywood, as stucco will absorb water. You will also need to attach the mesh with galvanized nails or lath screws so they don't corrode. There are two kinds of stucco: base coat and finish. For small jobs like this, you can probably get away with using just two layers of base coat. There are plenty resources out there on how to apply the stucco.
Best Answer
It sounds like your problem is stucco depth (1 in or more) versus drywall depth (1/2 in or 5/8 in).
Can you find a mud ring/box extender that's appropriately gasketed for use in a wet environment? If so, you can use that to bulk up the box depth.
You could also look for a deeper box. That one looks like a pancake.
Or, since you mounted the box on plywood anyway, just use several pieces of plywood to push the base of the box out to an appropriate depth.