Thank you for asking these great questions about the rules. If my answers aren't clear enough or you have other questions, please ask away!
1) Push: can I only push "from" (in straight line) or can i also move opponent character to sides or behind my pushing character?
Great question. The two spaces can both be in one direction or they can each be in a different direction. You can't push a character "through" your character (or any other character) since normal movement rules apply.
2) what happens if I push and pushed character would land out of board?
You may not push a character off the board. You would need to pick a different space to push them to.
3) what happens if I push opponent and he lands on tunnel?
You may move the character from that tunnel to any other tunnel.
4) Cowboy: can I pull my teammates?
Yes, you may pull your teammates.
5) Cowboy: can I pull every character in line (row or column) or only nearest one(who would "overshadow" next character in line)
You may pull any character in your lines (row or column) that may be moved 1 space toward the cowboy based on normal movement rules (so not blocked by wall or another character).
6) Athletic Businessman: can I jump over lying Flag?
No, you may not use the Jump action to move over a lying flag (but you may use the appropriate Run action to do so). You may only jump over walls or other characters.
7) Athletic Businessman: can I jump over trap?
No, you may only jump over walls or other characters.
8) Copy Card: if I play copy as 1st card: should I show 2nd card in first resolve, or should I do nothing in 1st resolve and make 2 moves in 2nd resolve?
If you play Copy with your first move without using one of your combo priority tokens (#3 or 6), you are not able to perform any action with the copy card. You do not get to “make up” for it in the second move. If you play Copy with #3 or 6, you may choose to play your second card from hand first before playing your Copy card.
9) What happens If I play move card and there is other character blocking my way? Do I just "loose" my move?
If another character occupies a space you try to move into, you may end up losing your move. If they are 2 spaces away and you play your #4 or #5 token, you may move as much as possible (1 space) towards the character. Keep in mind, if you use a boost you can move to the side to get around them.
Thanks again for asking!