You are asking a fairly deep set of questions that will take a bit of unfolding to address. I will address this in parts so as to not type a giant dull diatribe on molecular genetics. I will also keep it simple and just hit you with the general principles and not the details and exceptions but we can discuss anything you'd like in more detail.
So, lets start with the basics. What is a gene?
Roll this around a bit before reading on so we can properly air out your preconceived misconceptions.
Genes are discreet ordered sequences of DNA. This DNA is a long polymer made of 4 different chemicals which we can symbolize C,G,A and T. These 4 are the letters of the genetic code. All of the information to construct an organism is contained in this genetic alphabet. A gene is a functional unit of the DNA defined by it's sequence of A,T,C and G. The gene has a code for where it starts and ends. DNA is able to replicate so each cell in an organsim and each individual in a population of organism will inherit a full complement of genes.
Now ask yourself: What do genes do exactly? Think about this mechanistically. The easy answer is: Genes are the vehicle of heredity necessary to build and maintain an organism and it's descendants. But what about the mechanism, how do genes work and what do they really do?
Genes code for proteins. Proteins are made from long polymers of amino acids. It takes three DNA letters to code for a protein. This is the genetic code.
So if you wanted a gene that coded for nothing but poly-tryptophan the gene would look like:
AUGUGGUGGUGGUGGUGGUGGUGGUGGUGGUGGUGGUGGUGGUGGUGGUGGUGA
This codes for: START - (tryptophan)x16 - STOP
In general, this is all genes are and this is all genes do. To a first approximation each individual gene codes for an individual unique protein. Proteins actually do the work of shaping and maintaining organism. You are built of and by proteins. One gene, one protein.
Let me know if any of this is unclear. When you grok the basic principles of molecular biology the rest of your question becomes answerable.