1. I assume I can choose the target of a sentinel and it does not fire on my own characters (I didn't find it in the rulebook) ?
A sentinel doesn't have a target. The player who deploys it decides who or what it fires at, like any other unit. It just can't move.
2. If I have a character with a natural movement bonus (e.g. it cost only 1 to move through woods) and this character uses a mount, will the movement bonus still be valid ?
The characters are all slightly different, so it would depend on the exact text, but yes, probably.