1) A Walker is able to walk trough passages which are much lower than he is. How many pixels above the walker's feet have to be free to make him progress instead of stepping up or reflecting???
(I'm not sure I understand the question 100%.) The lemming will fall/drop if there is not a pixel at the same level of his feet. If there is a pixel at the same level of his feet, then he will step up if the height of the pixels above his feet are between 0 and 6, and will reflect and turn backwards if the height is 7 or more pixels.
Ex:
x o
x x
ooox oox
xxxo xxx
xx xx
The lemming will fall through the cracks in the first example, and step up in the second. ("x" is the terrain. "o" is the lemming.)
2) A Basher seems to stop bashing as soon as he can walk through the gap. On the other hand, he can bash even if he could continue walking, e.g. if we walks in a low passage. Is there anything known about the exact start/stop conditions for bashing?
I think it has to do with whether or not the basher would become a faller. If the decline is only a pixel or two, he won't, but if it is larger, then he'll stop bashing and will fall.
3) About bricks with arrows on them:
It's clear that a basher can only bash in the same direction as the arrows, but what about miners? I spend some time experimenting with miners in "Island of the Wicker people" and under certain conditions I could mine through the arrows from the wrong side, under certain conditions I couldn't. However I'm not quite sure what the exact rules are.
This is almost certainly a bug in the original Lemmings. Certain one-way arrows (I forget which), act as the opposite way's one-way arrows for miners, but not for bashers. It's actually a pretty stupid bug, and I'd imagine that you'd more likely want to implement one-way walls how they should be logically.
4) Bricks with arrows and explosions:
When a lemming explodes near to a brick with an arrow on it, these bricks are obviously not removed, if the lemming is standing on steel. Any clue what is the rule here? Are the bricks with arrows not harmed if steel is found inside the explosion mask or is it enough if there's steel beneath the lemming's feet?
The arrows are 100% irrelevant here. The only thing that matters is if there is a steel area underneath the bombers feet. Well, I'm not completely positive how falling bombers react vs. standing bombers, but in general, it has to do with steel at the foot of the lemming.
5) In levels like "Steel mines of Kessel" it looks like a Walker can walk through obstacles (plants) which are much higher than the altitude he could normally step up.
I would guess the reason is the obstacle's width. If it's small enough, it's obviously not accounted as obstacle.
Probably a second (or even more?) pixel is checked to see if this is a "real" obstacle. Any clues what the algorithm is here?
Each pixel height is checked separately. Any terrain strictly ABOVE the lemming is completely irrelevant! Only the terrain in the next line matters.
The structure in question seems to be this:
x
x
xx
xo
xx
ox
xx
ox o
xx
Now, imagine the lemmings as just a single pixel that rests on the ground (denoted by the "o"). Move one space to the right. Is there ground at his feet? Yes. Then is the height 6 or fewer pixels? Yes. So move to the next space. Repeat, and you will see the lemming should be able to clear this obstacle.
Just remember to ignore pixels above the lemming and it will make sense. If you just treat lemmings as a single pixel and ignore their apparent size, most of the games rules will make more sense.
And, ccexplore I'm sure will give you more detailed answers than those.