Can there be a position where a player has no move available? And if yes, what happens then? Can he pass and the game continues?

This position is probably only theoretical

How about this, white to move?

......bw......bb................................bb......wb......

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While it's probably very hard to reach this position, it's possible (at least I think it is.)

It is rather easy to come up with positions where one of the players has no move available:

. . . . . b . .

. . . . . b w .

. . . . . . b .

. . . . b . . . white to move?

. . . b . . . .

. b . . . . . .

. w b . . . . .

. . b . . . . .

. . . . . . . .

. . . . . . . .

b b . . . . b b

w . . b b . . w white to move?

b b . . . . b b

. . . . . . . .

. . . . . . . .

. . . . . . . .

. . . b . . . .

. . . . . . . .

. b . . . b . .

. . . . . . . . white to move?

b b . w . . . b

w . b . . . . .

. . . b . b . .

w . w b . . . .

In your third position both d4xd8 and d4xh4 are legal moves for white.

While it may be easy to come up with theoretical positions where one player has no move, the question is whether or not such a position can arise from actual play.

You are right about white being able to play d4xd8 or d4xh4. D8 should have been d7 and h4 should have been g4.

I believe such positions can be reached when both players cooperate, although I don't have proof for it.