I have pulled up the existing oak hardwood flooring and would like to re use it. The flooring was original in two adjacent rooms. At some point in time, a room separation wall and closets was removed, making one large room. The base of the wall was infilled with scrap wood and carpet placed over the whole thing. I am in the process of renovating and building a bathroom at one end. I ripped up all of the wood so I could start over without having the jog in the middle. Once I got all of the wood up, salvaged more than enough for what I need, I noticed they are from two different lumber mills and the tongue and groove are not compatible. New plan, use both types and incorporate a new pattern option in the middle with a frame on the outside. Here is the question(s) begin: I believe the pattern installation would be better installed in a glue down manner based on some of the small pieces that will end up being used...
1. Is it OK to glue every piece down and nail most?
2. The previous installation was nailed to the subfloor with old roofing paper between as a separation barrier. should I skip the barrier if I will be gluing?
3. The existing subfloor is 3/4" x 7 1/4" hardwood boards installed at a 45 angle with 1/4 ish gaps. Can I glue to this or do I need a solid subfloor?

Re-used flooring will have a special problem after it is fastened down the second time. Since the boards have been sanded and then moved, each board will be smooth, but not all the same thickness depending on where in the room they were located. This will be a challenge when sanding flat again since all the overwood will need to be smoothed to the thinnest board in the vicinity.
If you can find a pattern to be able to recover enough wood to be used in your spot you need to plan things well.
You can glue or nail the wood, but the tarpaper will have to be left out, and this is a moisture barrier that protects against moisture coming from below the floor, through the sub-floor. If the flooring has been acclimated then some seasonal difference in moisture content of the flooring ought not to effect it enough to be a problem.
The existing sub-floor will be adequate and strong, and stiffer than a plywood sub-floor of the same thickness. Just cross the sub-floor verses laying the flooring parallel to it.

Thanks. Should I install a 1/4" Luan as an underlayment?

I would only if I needed to lay flooring the same direction as the planks in the sub-floor and glue it down.

Yes, some boards will be running at the same angle as the subfloor.