The middle illustration is of a "Black Sallet" . A munitions grade Sallet made in bulk and used by Cavalry in the late 15th century. I have no knowledge of its use on infantry since all illustrations of its use is on Cavalry. Also, I don't know of any documentation of this style sallet being used by Landsknechts.
Here are some photos of pained Black Sallets:
Painted helms seem to be a mid to late 15th century fashion. At least that is what my research indicates. With minor exceptions to the helm Annie Lang posted. It is indeed a late period hybrid Sallet. There are a few extant examples, although most don't extant that I have seen have a paint job.
Now, that being said, I can't really say that landsknechts did NOT paint their helms either. It would certainly stand to reason that with the outlandish color combinations and ostentacious dress, that a landsknecht would paint his helm in outlandish fashion as well. I DO have a photo of an earlier Burgeonet with red cloth/leather covering it:
It's not a Sallet, but here's a helm that's painted yellow on the right side and red on the left.
It's at the Germanisches Nationalmuseum in Nürnberg.
Other painted helms were either just black, or black with yellow trim, or just yellow/gold trim.
I don't remember any with a double headed eagle (otherwise I would've taken a dozen pics of it).
I got lucky and obtained permission to take photos, but no flash and no tripod ... so the photos usually are not very clear, but certainly better than nothing, eh?