Should A Fan Do This?
 

My 93 is making some noises that sound like a bearing going out. I'm thinking it might be from my fan.
1) Should there be the amount of bouncing that you can see in the video? What part or parts should be replaced?
https://youtu.be/HDXU4YzZw7E

2) I've also seen where people have replaced the mechanical fan with an electric but I'm not sure how they wired it. Any thoughts on how beneficial that might be? I live in a desert so if it makes a worthwhile difference in cooling then i might consider it..
3) Thanks for any input.

Bad bearing. Take the tension off of the serpentine belt and you will know exactly what the problem is.

As I was driving this afternoon the fan froze up completely. I am thinking of replacing it with an electric fan. But with that and a light bar and whatever other electrical upgrades yet to come I'm worried about power draw on the battery. Should that be a concern? Will I need a bigger battery or something?

If you remove the mechanical fan you are still going to have to keep that pulley and bearing. So it needs replaced either way.

You will need some way to control an aftermarket electrical fan if you decide to go that route. Once you start adding major electrical equipment you will need to upgrade things like the alternator, cables, and maybe the battery. That's something for another thread.

I strongly suggest keeping the mechanical fan.

If the mechanical fan bearing is shot, you can replace the bearing. The part number is in the video.

Unless you are doing a lot of very slow rock crawling, keep it simple. The stock cooling system will serve you well.