Sounds like you may have multiple problems now!
Firstly are you sure you have the correct alternator fitted?
The KJ alternator does not have the Voltage regulator built into the Alternator but is regulated from outside by the Power Control Module (PCM).
Secondly the battery may now be fried if it started smoking.
Then there should be thick Dark Green or Red wire coming from the large lug on the alternator....this has a built-in "fusable link" which is like a fuse and could have blown while the battery was being cooked.
So assuming you have a nice new battery correctly fitted....you need a cheap Digital Multimeter, set it to DC volts and with one lead (Black) touching chassis or the negative post on the battery you should get + 12 volts shown when the other lead (Red) is placed
on the Red post of the Battery and on the large connecting lug on the alternator....if the voltage is not on this alternator lug then the Fusable Link is blown and your Alternator cannot charge the battery.
Now when you turn the ignition ON the panel lights should briefly light up then most of the warning lights should go out...oil pressure light only goes out after engine runs.
With ignition ON...put your Meter leads across the fuel pump....should show +12 volts as you turn the ignition ON.....Black wire is Ground (Black meter lead) and Dark Green/White is + 12 volts (Red meter lead). If this voltage is not there then move your Black meter lead to a clean chassis point to see if maybe your Fuel pump is not getting Ground. check #24 20 A in the fuse box under the hood and fuse #15 10 A on the fuse panel inside the cabin. Also try swap over the "Fuel Pump Relay" in the box under the hood with an identical one nearby.
Let us know the results of the above actions and we can take it from there.