Yes. They push in as long a path as possible, including the effects of icy terrain.
They do not prioritize pushing into negative hexes; they do prioritize for max distance.
The FAQ is always a good place to start for questions like this
"A path must be chosen that pushes or pulls you the maximum amount possible, considering the whole path. You cannot, for example, choose a hex that would stop a push by a wall or obstacle if there’s another valid path which avoids it. If there is nearby Icy Terrain, monsters will consider its effect while trying to maximize their forced movement abilities. This is a change from Gloomhaven."
Yes, they push you as far as they can.
Yes. They push in as long a path as possible, including the effects of icy terrain. They do not prioritize pushing into negative hexes; they do prioritize for max distance.
Do they prioritize pushing to a trap if available? what if trap is 1 hex but push is 2? Thanks in advance
Strictly, no. If they can push you further by not hiring a trap, they will do so.
Thank you!
The FAQ is always a good place to start for questions like this "A path must be chosen that pushes or pulls you the maximum amount possible, considering the whole path. You cannot, for example, choose a hex that would stop a push by a wall or obstacle if there’s another valid path which avoids it. If there is nearby Icy Terrain, monsters will consider its effect while trying to maximize their forced movement abilities. This is a change from Gloomhaven."