I have a 99 Qx4 took alternator off to be tested. Hooked back up now battery sparks when hooking up. Theres a short black wire hanging by alt. Should this be hooked to alt

if the alt is working then there may be a draw on the electrcal system when the key is off ,and pulling the charge out of your battery in time,a good way to ck. this is to first unplug the underhood light then unhook the positive battery c able use a 12v.test light between the battery and the unhooked cable if the light is on there is a draw go to the fuse pannels (under hood &under dash)pull one fuse at a time till the test light shuts off,that is the curcut with the draw,then look for shorts ,no ground and ect.

The battery needs 12.6 volts or more to be in service
When the engine is running you need 14 volts or more
out of the alternator to charge the battery
You can test the alt by testing across the battery term
or the alt output wire & ground to case or motor
Could be the diodes got fried & you need a new alt
Have it tested at parts store, if you can't figure it out
Check all fuses & fusible links first

What is the output voltage of the alternator with all the lights on and the heater blower on high and the engine at 1500 RPM?

Your pos and net wires may be crossed on the alternator

Yes a bad battery can cause this problem. Pull out the battery and take it to have check also. But, your wiring to the alternator maybe at fault. If your alt. is good but, it is not charging the plug or a wire may not be making contact. Check your battery. Check for any broken, burnt loose wiring. I know you just had it out. But check the wiring at the battery. The smaller wires are whats called "fusible links" meaning they are fuses. Tug on them a bit to see if inside the insulation you can feel the wire separate. Hope this helps Fix Ya up.

Check output from alternator with a voltmeter it should be between 13.8 to 14.7 if so then check at battery if it is not at least 13.8 minimum to be charging then the big wire on back of alternator is not getting back to the battery through ammeter gauge in dash.
I have hooked a wire from back of alternator straight to the plus[+] side of battery to fix that issue.
Sometimes ammeter gauge burns out breaking the circuit from the alternator back to the battery.

small short in wiring. test by taking each fuse out one at a time and look for spark as you put back in (with battery charged and hooked up). circuits drawing current will spark. Narrow down to circuits that shouldn't be on when the key is off but spark at fuse.

Very probably a bad charging system. You might need a new altenator.

need to have it tested to see if there is a diode in that system they pluginto the fuse panel under thee hood like a fuse but it says diode on top? also have wiring tested at alt make sure you have 12.6 volts at big wire on alt? hope this helps

First check alt At The Back of Alt Big Red Wire Were hooks to Post (stud) Do you have voltage ?? How Much??
What Voltage do you have at same Place with Engine Running ??
Now At wires Were they plug into Alt ,Top. Wires in White Plastic Clip, Do You Have Powe With Key On ?? How Much Voltage??
Jump across the 2 in the clip (with Engine Running)ONLY TEMPORARY!! Do You Have Voltage at Battery ?? How Much??
If Over 13volts With Clip On (Jumped) You Need A Internal Voltage Regulator ..
Is Batt Light On on Dash ??? Theres A Lot Of Testing You Can Do !!! And I will Need More Infomation to Keep Going ... These are just some Possible Problems No Way In Depth ...
Could Be a Number of things Or May be Just as Simple As a Blown Fuse, Dirty Batt Cables ETC etc etc I Hope It Puts You On The Right track !!!!!!!!!!