Im trying to remov a hormonic balancer on a 1989 acura legend

No, it is not. Acura, and Honda Harmonic balancers, (the crank pulley), come off fairly easily once unbolted. Sometimes you have to pry on them a little, but I've never had any difficulty removing them.

Probably your fuel pump. If its EFI remove the cap from the shreader valve on the fuel rail and turn the key to the on position. Listen to see if you can hear the fuel pump kick on. Leave the key on and press the shreader vlave. if fuel doesn't come out hard and strong then either it's the pump (most likely) or the fuel pump relay might be bad. That relay can be changed with other relays of the same part number in the fuse console under the hood. Try switching it out and see if the car starts. If all that checks out good then the next step I would take is to look at the cam / crank sensor.

Lower front of engine derictly behind hormonic balancer IE the lower pulley on engine but before the oil pan two wires fairly easy to replace

You need a puller.

Check it through a couple of rotations to make sure the cams are aligned. You will need a good manual. This is a complicated + $500 job. Since everything comes off, do the water pump and all of the belts at the same time.

If the year is the same, the colors should be the same. There are diagrams in Chilton or Haynes manuals but they can be misleading. Remove enough tape wire so you can see the color(s) and re-check before you electrician tape everything up. To be slick you could use "shrink" tube insulation. Work on one harness at a time. Elect.windows and mirror should be separate "feeds".

look for the wire that is on your exauhst that is where the sensor is! it shouldnt be very hard to replace it yourself.

yes you should always have the cam sprockets aligned with tdc and the engine should be on tdc whenever removing or installing the heads.

if the battery drains dead there is a leak in the wiring some were
some thing is not turning off