NH is distance-based, AC is zone-based so the cheaper one depends on where you live and where you're going.

All *A partners have the same access to a certain common *A inventory. However, some carriers may pose restrictions on their own members by blocking awards (like UA and probably US) or they can release very few or limit the types of award inventory released to the whole of *A and make additional award space available for their own members only (SQ and I think LH). All *A awards are at the saver level.

The simplest answer to your last question is no, you will see the same availability from all FFPs, especially for that route.