How can I program random lights, lightning, and intensity change

Yes effects can and mostly should do those things. While there are several ways to do most things, effects are ideal for repeated changes. Whatever you do keep a show file with your effects so you can retrieve them and build on them in future shows.

This shot is my standard lightning effect. I built it for fixtures with a strobe channel but decided that the regularity of the flashes was too noticeable and that the flash duration was generally too short. You may choose otherwise or even build several variations.

This effect is a disco party look. All channels chase through color palettes but each channel is a random color. A few tweaks and you could have a random flash. Perhaps intensity palettes or presets with just one fixture on instead of the color palettes.

Random brightness is a bit harder. You can't have more than one effect on a single parameter at once. Without a better idea I'd do something like the color one above, but use a really long list of Actions and just type in a seemingly random list of times and levels. That way there would be very little repetition and so the audience wouldn't notice. Theater Magic!

More than anything, don't forget to put StopEffect (>Effect Enter) in the next cue. It's a common mistake.

Likely someone else will chime in with their methods! That's part of why I hang around here, I learn a lot from everyone else.