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).
I wouldn't start cutting out chunks of drywall to fix a small area like that.
Take off the wall plate and remove any loose or crumbling drywall. Apply a piece of fiberglass tape over the area, mud, sand and repeat as necessary to get a blended finish. Then prime and paint to match.
The fiberglass tape is nice for repairs like this because you can stick it to the wall and then mud on top of, unlike paper tape which you need to apply on top of mud. I've fixed a bunch of similar defects like this and several years later there are no cracks and they look great.
Best Answer
A proper electrical box is the only way to do this. You CANNOT simply cut a hole and pass the wires through. Any and all line voltage (120/240V and up) splices must be in an approved box and be accessible, meaning you cannot bury a junction or splice box. I could cite all sorts of relevant codes but I don't think that's necessary. This should be obvious.
Here is a recent thread on this very subject: What type of electrical box do I use for a hard-wired smoke detector?
Remember, it is almost a certainty (code wise in the US) that an AFCI breaker is required.