Turning publicly available genome data into proteins
No, your approach will not work, you are taking a very simplistic view of an extremely complex system. Some of the problems you are ignoring are:


Genes (eukaryotic genes anyway) are spliced to produce mRNA, a process that removes introns and leaves only the exons. If you just translate the entire chromosome file you will get noise. 
Splicing also changes the frame a gene is read in, you don't mention frames at all in your question but you can't work with sequences unless you deal with them.
Many genes (most even, in some species) are alternatively spliced. One gene can give rise to multiple protein sequences. Which one is produced at any one time can depend on a multitude of factors ranging from pure chance, through environmental conditions to the cell type where the gene is expressed.
Genes can be present on both strands of DNA and a gene on the + strand can overlap with a gene on the - strand. In some cases they can even overlap on the same strand (nested genes). You need to check both strands for coding sequences.
You're assuming that all coding sequences start with ATG (most do, not all) and you seem to be assuming that an ATG always starts a coding sequence. A given gene can have dozens or hundreds of ATG codons, how can you know which one is used as a START codon? 


The process of identifying the parts of the genome that get translated into protein is not trivial. It is the subject of countless PhD theses, mine for example. There are many programs (gene predictors) that are designed specifically to detect genes in genomic sequences. Having spent many years working with them I can assure you that they're not something you can just whip up one afternoon. They tend to involve very complex models of coding vs. non-coding sequences and are way more sophisticated than simply looking for START and STOP codons. Trying to write one without knowing a lot more about biology than you seem to is just a waste of time.

Your specific questions are basically irrelevant because of the points mentioned above. Nevertheless, the answers are:


They vary but not much. For well annotated genomes like the human one, the differences will be negligible. That is not why you have strange results though as I explained above. 
All public FTP sites tend to have a README file that explains what the files provided are. You should read the relevant README from ftp://ftp-trace.ncbi.nih.gov/1000genomes/ftp/
Answering that question will get you a Nobel prize. There simply is no way of predicting what genes will be activated in a particular cell. We're not even close to that level of understanding of how a cell works but I can tell you that it will not depend on the sequence, you will never be able to predict whether a gene is active in a particular cell based on its DNA sequence. It will depend on various things including the gene's methylation state and is largely an emergent quality of the cell's complexity (think of various proteins interacting with one another, leading to the activation of a gene).  The best you can do is get a list of genes that are known to be active from the literature. 


In summary, if you want to do something as complex as modelling a cell I suggest you first take the time and study some basic biology so you can understand the system you are trying to model a bit better. The cell is not only an extremely complex system that we don't fully understand yet, it is also not wholly deterministic and contains a lot of stochasticity that you seem to be ignoring completely.