The Hifiman HE 400i's as well as the HE 560's are prone to having the forks (the part of the headband that attaches to the earcup) break. That is what happened to me, so I decided to print out a replacement.
I tested various materials, and I will list the viability of each for your convenience.
PLA: it holds, but the material is rather stiff and brittle. It will work, but I would recommend something with more flex.
ABS: This is what I am personally using (matterhackers burgundy) ABS has good flex, is stiff enough to not give, and has a good temperature resistance.
PETG: A good alternative to ABS, has a bit more flex, which may be desirable. Less overall temperature resistance.
Nylon: Too flexible, it doesn't provide enough clamping force to stay on reliably.
I have used the ABS parts in the picture (the burgundy one) for over 6 months, and they have proven to be much more durable then the stock forks.
You will need to unscrew the plastic hinge that attaches to the swivel point of the forks, then rotate the forks to release the adhesive keeping them together.
After that, attach the forks to the earcups (they have enough flex to be stretched and snapped into place and put them into the hinge, then screw them back on.
There will be various pictures showing off different colors as well as the fit of the swivel part.
Doesn't matter too much. Try to keep it under 300 microns (0,3 mm).
Doesn't matter as long as it isn't garbage. ABS or PETG is recommended, but if you can only do PLA, it should work.
Whatever looks good to you.