If you're talking about an E26 lampholder (the medium screw-in base widely used in the US), there are only two electrical contacts: live is at the back of the lampholder and neutral is the screw thread. While the light fixture itself should be grounded, it's not available via an adapter.
In an outdoor situation, ground protection is even more important than indoors; if your exterior circuit also includes exterior receptacles, it should already be covered by a GFCI. As I said in an another answer, that breaks the circuit if there's a ground fault, but without a ground connection, any current is going through you to ground, instead of through the ground lead. So no, it's not safe to use a two-prong to three-prong adapter and leave the ground on your lights disconnected.
I have seen exterior light fixtures with a grounded electrical outlet built into them; if you were able to change the light fixture, that would be the safest way to go.
Outdoor Power - Do not power the camera using an outdoor outlet. You have all the problems you listed and you make the system more susceptible to tampering (an intruder can simply unplug the camera and blind the system).
Powering the camera - Let's begin by checking if the camera and its power supply is rated for outdoor use. The exposure to moisture, and to a lesser degree extreme temperature, makes many indoor units unsuitable. The connection of the power supply to the camera needs to be water resistant. If it is not, you need to consider a different camera unit.
In general, outdoor power lines need special cable or a metal or plastic pipe to protect the cable. The power to the unit is apparently low voltage, so it may not need the same level of protection as it would if it were 120 volts.
You will need to bring the wire through the wall (or through a soffit) at some point. You want to drill through an area that DOES NOT contain framing. You will go through siding, sheathing, probably insulation, and then finish material, probably drywall.
The main issue is sealing the entry holes from water and air infiltration. This can be done on the outside using a good outdoor caulk.
On the inside, you can use a low voltage junction box to protect the wire and then route it to an outlet. The best approach might be to run the wire to a double box, low voltage on one side and line voltage on the other.
You could then have the wire exit the front of the low voltage side and have the transformer plug into the line voltage side.
Mounting Camera - Most modern cameras (at least those without heavy housings or motor mounts) are fairly light, just a few pounds, if that. They can be screwed into the sheaving of the wall, which is located beneath the vinyl siding. You need to drill through the siding and into the sheathing and then screw the base to the sheathing. As you are mounting, you can seal the screw holes and even the base of the camera with outdoor caulk.
If the camera is heavy, you should screw the camera to a framing member (stud). These are found at corners, regularly spaced horizontally (usually every 16 inches from a corner), and near the roof and floor line of each level. You can use a stud finder to locate them.
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Those waterproof covers are only rainproof. They are open at the bottom for the cords to go through so they are not moisture and humidity proof. Outdoor rated cords have a heavier, much heavier, insulation to protect them from the outdoor environment, sun, UV, animals,etc. The male and female ends are also insulated heavier and are of higher quality. Connecting to a weatherproof box is not the same as indoor use and if the outlet is outdoors, it will have to be GFCI protected.