Does that means that there is no way to keep the anchor when there is a clash, except if the clashed cards were phase shift?
Just to be clear, you only lose the anchor if you played an action that clashed with another player. That is if two other players clashed amongst themselves, you keep the anchor (since you're not involved). That said, if you are indeed involved in a clash, there is no way to keep the anchor.
Also is it the case that I must resolve the action when I give up the anchor - it's not optional?
If a clash occurs and you hold the anchor, you must give up the anchor and resolve your action. You may choose not to perform the action, but the card is still considered resolved.
Although I like the game, I don't seem to have managed to play it much and have found this a tricky game to teach people, mostly due to my own lack of playing experience. Have been trying to get the rules as clear as possible in my own head as have made a few mistakes along the way...
We've found players who have experience with competitive card games seem to pick up the game much quicker than other kinds of players. The simultaneous action mechanic can be tricky to wrap your head around at first. Generally, new players pick up the game pretty quick after a couple rounds of play, though.
Hope that helps!