Once at sea, how does Pi draw upon his experience with animals, and his faith, in order to survive? And, how does his success reflect the contradictions and balance in his view on life?

This question is asking more than one thing, so this answer will address the first question in the post.
Once Pi is in the lifeboat with Richard Parker, he is forced to draw on the knowledge that he obtained from being around all of those animals at the zoo. I would recommend going back and looking over chapters 13 and 14. These two chapters have Pi explaining to his readers the concept of the "alpha" in any group of animals. Pi tells readers about how a lion tamer must present himself as the alpha in the ring. That way, the lion looks with fear upon him and respects that leadership.

They are in the presence of a strongly dominant male, a super-alpha male, and they must submit to his dominance rituals. . . .
Only the trainer better make sure he always remains super alpha. He will pay dearly if he unwittingly slips to beta. . . .
It is interesting to note that the lion that is the most amenable to the circus trainer's tricks is the one with the lowest social standing in the pride, the omega animal. It has the most to gain from a close relationship with the super-alpha trainer. It is not only a matter of extra treats. A close relationship will also mean protection from the other members of the pride.

Pi takes this knowledge of the alpha and lions and immediately begins working to find ways to signal to Richard Parker that he, Pi, is the alpha in the boat.

I had to devise a training program for Richard Parker. I had to make him understand that I was the top tiger and that his territory was limited to the floor of the boat, the stern bench and the side benches as far as the middle cross bench. I had to fix in his mind that the top of the tarpaulin and the bow of the boat, bordered by the neutral territory of the middle bench, was my territory and utterly forbidden to him.

As for religion, that is what gives Pi hope and mental strength. Pi even foreshadows to readers just how important religion is to him (and how useful it will prove later in the book) when he tells a teacher just exactly what religion will do.

"Religion will save us," I said.

Readers get to see just how much faith and religion really do save Pi in chapter 53. We get a great quote that shows just how much Pi is digging into his faith reserves to give him hope each day. The quote also shows that religion and religious practices give Pi a routine to keep his mind active while on the boat.

I was giving up. I would have given up—if a voice hadn't made itself heard in my heart. The voice said, "I will not die. I refuse it. I will make it through this nightmare. I will beat the odds, as great as they are. I have survived so far, miraculously. Now I will turn miracle into routine. The amazing will be seen every day. I will put in all the hard work necessary. Yes, so long as God is with me, I will not die. Amen."