Electrical wires typically run either vertically, up and down the side of a stud (with staples), in order to reach receptacles, ceiling lights/fans, etc., and horizontally in order to get across the room(s). The vertical wires are typically pretty easy to avoid: avoid drilling/nailing above a receptacle or light switch, or, if you have to, avoid missing on the side that the receptacle is nailed to. The horizontal runs should have enough play in them to avoid most damage, unless you drill/nail into the hole in the stud (called a nipple) that they pass through.
I don't think that it's required that you put any metal plate on the stud in order to protect the Romex/cable/conduit, but rather that it is only required if you drill the nipple too close to one side of the stud, at which point a metal brace is needed in order to ensure structural strength. Outside of drilling/nailing into an unprotected nipple, or very near it, there is little to worry about when it comes to the electrical.
When it comes to pipe, you should be able to tell if you hit copper pipe. Even though it might be one of the softer metals, it's still going to offer a substantial amount of resistance, and unless you hit it where it passes through a stud, your nail/drillbit will probably deflect off of the curved surface of the copper pipe. With PVC or ABS, however, yeah, you're most likely going to have a leak if you hit it squarely with a drillbit, maybe even a nail.
When it comes to cutting large holes in drywall, cut horizontally first -- if there's a stud or vertical pipe, it's better for you to find it immediately, at which point you might decide it's better to make a new hole on the other side of the stud, rather than later, after you've already made a long vertical cut in the drywall.
It's difficult to model the situation with rational analysis, there's too many intangible factors. You could do an empirical test. You need to support 20 lbs per fastener. We can apply a safety factor of 3 for ultimate strength, so the fastener should support 60 lbs without actually breaking. So you would need 2-4 fasteners to support your weight. Round down to the closest whole number. Install the clips as you did in the wall, except now install a metal strap between the screw head and clip. Arrange the straps so you can step into them to weight the system. Arrange the straps such that your weight is distributed evenly to each fastener.
Weight the system and see if they break. If you live in a seismic area, bounce on them a bit and see if they break. You'll either be able to sleep better or you'll know what to do next, depending on the outcome. Obviously there are better ways to set up an empirical test, I chose to illustrate a quick and dirty method just as an example. Be sure you are protected from flying shards of metal.
Regarding an increaser for the number of fasteners. No, you can't do that. It is a valid concept though, for example you can use a higher allowable bending stress in multiple floor joists than you can in a single use situation such as a header. The concept is not generally applied to fasteners.
Response to OP's Update
Shear strength in relation to fasteners partly depends on what the fastener is holding. In this case it's known as a metal side plate condition, meaning the expected failure mode will either be the top of the screw failing through the shank (shear) or the wood collapsing under the compression from the screw. It's rare in reality to have a perfect shear condition, there is usually some bending and tension components as well.
A true shear condition would something like a metal strap screwed to the wood surface and all the force was parallel to the wood surface, exactly perpendicular to the screw shank. In your test, you mostly have the vertical shear component, but there is a tension component as the center of mass is away from the wall surface. We can safely ignore the tension component in calculating a working load since 80# in pure shear is more conservative than 80# shear and, oh... say 15# tension combined.
A picture of the clip was helpful, I imagined a much worse condition. Either way, the ultimate strength will not be proportional to shear alone, there are other factors difficult to model, thus testing is the best approach. The failure mode you experienced is a bending failure, but your actual installation, while having a bending component, is in fact mostly a shear condition.
The duration of load is a factor. The usual allowable stresses specified in construction are for permanently applied loads. The allowable stresses can be increased for shorter durations, 15% for a few months, 25% for a few weeks, 33% for a few minutes. Meaning we should reduce the allowable load determined through short term tests accordingly. But we also don't know the ultimate load since you didn't achieve failure. Just as well, uncontrolled destructive testing can be a little too exciting. You also haven't run multiple tests (I assume) to confirm you are getting consistent results.
Let's say you did run multiple tests and they all actually failed at 80#. When you apply the 3x safety factor, then adjust for duration of load, you end up with a working load of 20#, exactly what you need. Considering there was no failure experienced, and the installation does appear to be predominantly shear, I think your installation is safe. Barely. Next time around, use heavy ordinary wood screws ;)
Best Answer
Nail isn't exactly safe if you are directly nailing. Chances of something happening are small (and really much greater chance to damage line than "shock" yourself) but it is there. Also I doubt a nail would hang the calendar without eventually sagging. Calendars are touched and moved and not ideal for just a nail - unless you can get that nail in framing.
Monkey hooks should be about as safe as it gets. Don't hit them or press them in. Screw them in slowly (I know there isn't threads) and once you pierce the drywall loosely move the main shaft up. If you aren't applying pressure to it once it is in even if it hit a line it should not nick or pierce it. I would go this route if you have to have the calendar in this exact location. Monkey hooks are very strong and not invasive to your walls.
If you want to be extra safe with Monkey hooks you can bend the tip so it isn't sharp on the end once you get through the wall.