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.
![dual voltage box](https://i.stack.imgur.com/bdtsa.jpg)
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.
Use a magnet to identify the outline of the metal.
It could easily be a nail plate:
![Nail Plate](https://i.stack.imgur.com/mNxK2.jpg)
The purpose of which is to protect wires and pipes, from you.
Best Answer
Your primary concern will be that you're putting a hole into the outside of your house that will let water (and bugs and, possibly other things) into your house. Therefore, it is critical that you ensure that when you're done, the hole is water tight. Water leaking into the wall, especially if it's a wood-framed house will lead to rotting out the sill and studs, and the cost to repair that in a few years will be much greater than that of going to the gym to do your pull-ups.
The second concern is to ensure that the bar can support significantly more than your weight. Any jerkiness in your pull ups (on the way up or down) will exert more force than just your weight. To this end, you need to ensure that you're attaching to a stud (if a framed house), or that you're attaching into something solid (if a brick or block) house. If you've got poured concrete walls, your only concern (once you have a hole drilled) is ensuring that you've got a solid connection (use proper concrete toggles). Also, consider that once you've got this handy bar right next to the house, that you (or someone else) may use it for hanging other things of considerably greater than human weight on.
An additional concern is that at some point you may want to leave the house. This would mean selling (I presume you're not renting or you'd be asking the landlord about this). Is the next person going to want a pull-up bar attached to the outside of his house? Sure, it could be removed, but then you've got the stub where it was cut off, or holes where screws/bolts were removed. Might not look all that pretty when you (or they) are done, and make it more difficult to sell.
You may consider mounting it to the cinder block wall like a towel bar instead of crossing the span between the house and wall.
Oh, yeah, one more thing... Is that cinder block wall yours to be drilling into? (Just checking...)