That's a lot of questions. Many are better answered by Youtube. I like William Strife's Minecraft series. https://www.youtube.com/...Luo9LGfj5o
-How to get diamonds very fast
You generally won't be getting diamonds fast. Diamonds can only be mined by an iron pickax, which requires iron ore, which can only be mined by a stone pickax, which is made of cobblestone, which requires a wood pickax.
Once you have found Iron, dig a long downward passage until you are between Y level 16 and 12. (Or about 12 levels up from the bottom of the world. Then just create a one block wide and two block tall tunnel in a flat direction. You will eventually either run into diamonds, or into a lava chamber which will generally have diamonds in it.
-How to find food fast
In most biomes, knock out leaves from trees, this will usually create apples, which you can eat. If you get lucky you can find a village near your start point and get carrots (which you can eat raw), wheat, and potatoes (which you can cook.
-Where to find animals like wolves and cats
Wolves, cows, sheep, and chickens spawn basically everywhere on the surface (except deserts) pick a direction and explore long enough and you will eventually find one. Cats only span in the jungle.
-Special tip
Once you build a house, or start a base, get its XYZ numbers or mark it in some way so you can find it again after you are killed.