Blinkers don't work, wipers don't work.
 

And I can't get the headlight's high beams to turn on. I figure this is about a bunch of blown fuses.

Since I've had the Z (relevant information) I've removed the battery to rip out the old battery tray and replaced it, rewired the fan's wires after they had been previously hotwired to the ignition. I tested the blinkers before, one side worked and the other didn't. I finally reconnect the battery and neither works now.

Can anyone walk me through this and explain what needs to be replaced? Thanks for any help.

Best thing to start with is checking your fuses.Move out from there to all the wiring - including the grounds(do the low beams work?).Since the PO played with the wiring i would pay very close attention to all of it.
When you move the stalk switch left or right do either the front or back turn siganl come on?If you have a bad bulb the turn signals won't flash they just come on.Also you could have a bad flasher unit which is mounted under the dash to the right of the steering column behind the ALDL port(Chevrolet calls it the conveince center - seat belt/key chime and horn relay are in this location too).
When you changed out the battery tray was the side marker light wiring cut or frayed.i ask this because it runs very close to the battery tray(acid could have gotten on them at some time).
Do the brake lights and emergency flashers work(flasher module is also located similar to the regular flasher unit although closer to steering column)?They are on a separat supply circuit but use the same branch wiring(at least for the flashers).

I didn't even try the horn yet! I also have to check hazards. Thanks for reminding me.

The flasher lights don't come on and you can't heard the "click,click,click" at all. They don't come on in the back or on the front and all of that should still be connected. I know where acid splashed before and had to replace a couple fan relays. I didn't replace the wires though, I found them taped up...
Let me see how much works and then I'll update.

UPDATE-
Hazards work COMPLETELY and the horn works half of the time. If the hazards are perfect, that can only mean that everything that lever on the steering wheel is attached to has gone bad. I did a walk around and all the lights come on, I need no new bulbs. What do you suggest?

That still doesn't explain the high beams...yet

Here's the update, I had the car's power off, now the here's what works, the right flasher works slower than the hazards, the left flasher turns the bulbs on but doesn't work. The wipers work but i'm having a hard time turning them on.

No high beams yet.

As I stated the flasher module,horn relay and seat belt/key buzzer are located in the "convience center" behind the ALDL port.The hazard flasher is mounted closer to the steering column.
If your'e trying the turn signals without the car running they will seem slow.An incorrect flasher module or a heavy duty bulb will cause this as will low voltage - less than 12.5VDC.Your left side not flashing could indicate a bad bulb.Do all 3 bulbs light up with the turn signal activated?Remember the front marker/turn signal is a dual filament.Even if the park light works the bulb could still be bad.
Your wiper problem could be a stalk switch problem or a motor problem(something as simple as a bad ground).The high beam switch is located on the steering column,on top I believe,under the dash.
Also have you checked all the body grounds?This could be a root cause of your problems(especially the 14ga ground going from the battery to the fender).There's also a ground from the firewall to the block.And of course the main battery ground to the alternator bracket.