Im at the last step of installing my 1/2" engineered bamboo floors and ran into a problem. I ripped up the original hardwood in the downstairs of the house and replaced it with the bamboo. I was going to do the same in the upstairs hallway however they original hardwood is nailed directly to the joist.

I would like to have the new bamboo running parallel, the same direction of the hardwood. The hallway is about 8ft x 4ft. Without ripping up the hardwood, can I put down a 1/2" underlayment then the bamboo or do I have to go with 3/4"?

You can do half inch, 3/4 is the minimum thickness of a subfloor.

What about this...since the there is 3/4" tongue and grove hardwood nailed to the joists and such a small area, would it be OK to screw each piece of hardwood to the joists with screws then install the wider plank bamboo over that?

If you have had no problems with the bamboo downstairs it should be good fastened just like you have in the downstairs. Acclimate it before you install to get the best results.
If you know which side of the hardwood is fastened, then nail or screw the other side of the T&G