I have a question about Hidden Vale Pass and save effects.

Hidden Vale Pass

Text:
Westeros Any Phase: Kneel Hidden Vale Pass to put a Clansman character into play from your hand, knelt as an attacker during any challenge you have initiated. At the end of the challenge, discard that character from play if it is still in play.

Can you save a character from being discarded because of HVP's effect? I am unsure about the answer since they wrote "At the end of the challenge".

In other words, do the same rules apply for "At the end of the phase" and "At the end of the challenge" effects?

No, this "end of the phase" rule does not apply. It is an exception detailed in the FAQ that should not be taken as a general rule.

The end of the challenge is a normal framework where the result of challenge is implemented.

So yes, you can save your clansman.