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Q: I assume since these are pipe thread that no pipe dope or tape is needed (or desired) on the threads, right?
One end is pipe thread, and will seal without teflon tape or compound.
Q: Which tap would I use for 268-no6x04?
You would need a tap for 1/8th NPT.
Q: What is the difference between this part which is part number 268-N04X02 and another fitting which is part number 12-05471
They are just from different manufacturers, they will both work with nyloseal.
Q: Will NYLO-SEAL FITTING 268-N04X02 screw into standard Altimeter, VSI, and Airspeed indicators at its input
If those instruments have 1/8 npt ports on them yes. That is the most common size.