Do the trip mines only trigger (token gets revealed) if a hero ends his turn on the token or also if he moves through/over that token?
Ending the turn on the mine does not trigger it. You have to either move on to the mine, or off the mine on your turn in which case it's reveled instantly.
No, it's not.
Simply follow the card's text
On his turn, if any hero moves to or from the space with a token, reveal the token.
Which means, if you end up on a hex with a mine during some other player's turn (thanks to some other hero's actions) the mine will not explode, as long as you don't move from that space on your turn.
And since all tokens are removed at the end of the round, as long as you manage to not die from something else, you'll be fine.
The second situation could arise if a hero wants to reach the space behind a mine, but can't do so without moving over the mine, because the other spots are blocked by units.
As soon as you step on the mine space on your turn, it's revealed.
The only way to move through a mine without revealing it is by using some skill which allows you to "ignore obstacles on the way", such as Steam Jump or to use Teleport which places you directly to a space in range.
So if the mine is blocking your way, you have to either take a risk and hope it's a dud, or find your way around Blocking-off paths for the enemy heroes is the primary use of Min's mines.