How to get the crew to stop cheering

On the minimap a rogue wave icon does appear and shows which direction it is traveling. And to avoid losing crew members you hold the 'X' button(on Xbox), Space on PC, Y(on Wii U), or Square(on PS3) but that will brace the crew and you won't take as much damage.

Also, You can get more crew by going to a tavern, helping pirates in the locations, or picking up castaways in the open sea.

As some have stated in the comments, another way to avoid damage from the rogue waves is to face them head on. But in my experience it is just easier and quicker to brace and then get back to the battle.

Destroying ships yields only half of their cargo. So, it's generally better to board them. If a ship has gold, sinking it will still give you all the gold.

And, as you suspect, later on you will be able to capture ships and send them on missions to earn credits.