I am new to this forum. Pardon if this reply does not post correctly as I am not particularly cyber-savvy.
Question 1 was about the meaning of the term "faith". Simply, faith is belief put into action. Within the Christian context, it is going beyond merely believing that Jesus Christ is the Son of God and died on the cross for the sins of the world, for any who would accept Him as Savior. That is merely belief. Faith is putting your trust in Him on whom you have believed to save you. It is putting your belief into action.
An illustration I once heard from a preacher: There was a man who could walk a tightrope. He had great skill, was not bothered by heights and could carry any number of things in a wheelbarrow along with him as he walked the tightrope way up high. This man was so skilled that he strung a tighrope across the Grand Canyon itself and walked out there, so high above that chasm. The people gathered to watch and they were amazed that he was so very brave. This man was quite a showman so he gathered a stove in his wheelbarrow and some food and went back out over the canyon and made himself breakfast! The crowd gasped in fear and delight. When the man came back to the edge, he asked the crowd what they thought of his skill. They all exclaimed how much they were impressed by him. Once man in particular stepped forward and said "I believe you could carry anything, anything at all in that wheelbarrow on that tightrope. The tightrope walker looked at him, pointed to the wheelbarrow and said "then get in".
The onlooker did say he believed the tightrope walker could carry anything in the wheelbarrow. But to get in it would take faith.
Question 2 was about the difference between man and animals. You mention that you want the answer to exclude Genesis but this is the key to the answer! Study Genesis to find that the animals were spoken into existence in the same way that the earth and the heavens were made. But man was fashioned from clay, made in the image of God, and God did breath life into what He had made and man thus became a living soul. This is a fundamental difference between man and animal.
Philosophers have long debated along these lines and their answers have drawn such conclusions as: an animal cannot contemplate its own demise or origin, an animal does not aspire to greater things, an animal cannot imagine beyond its own experience and etc. Such things are depicted in Scripture as being within man's capabilities and certainly we all do these things.
Love them though we may, Christ did not die for animals. But He did die for you in order that you could be restored to what you were created to be. Accept Him for what He has already done for you and claim the gift that is eternal life.