Is the start conditions also known? Obviously it's not the same condition as a Walker can be converted to a basher if there are pixels in front of him even if there are free pixels below them (small passage as explained above).
Well, it's time to check your e-mail.
But in short, there is no "start condition". The basher will always bash at least 1 stroke before quitting, even when there's nothing at all to bash. Although the game does prevent you from assigning the basher in the first place if you're too close to steel (don't have the exact condition at hand at the moment).
And what if the basher can step down? Will he continue bashing if e.g. the fall distance is 3 pixels or less (like a Walker would continue walking)?
Check your e-mail, but it's 2 or less as Shvegait stated, and yes he will continue bashing.
I've actually seen this in action even on the regular, official Lemmings levels. So it's not really too hard to verify at all.
This is strange if you consider how even animated objects like the exit in "Lost something?" are drawn on a by pixel check with the collision mask.
Yes, but remember there can be up to 80 (or 100 in some versions) lemmings. Whereas the number of interactive objects are much lower, not to mentioned that the interactive objects outside what's currently displayed can simply be not drawn.
I wonder if I should adapt this strange behaviour as it seems to be more like a bug.
I would consider it more of a bug.
But it's up to you. The original Lemming's game mechanics certainly has its, um, weird points. I think at last count there are at least a dozen or so of these "weird points".