where to find the relative frequency distribution of synonymous codons
The phenomenon of using different codons with different probabilities is called codon usage bias. How the different codons are used is sometimes pretty different between species and requires some care. This is especially true when you want to overexpress sequences in bacteria to produce protein, which may need codon optimization to ensure an optimal codon usage (otherwise rare tRNAs can slow down the translation process). There is a database (based on the NCBI Genbank) which gives you the codon probabilities for different species:


Codon Usage Database


Additionally, these papers might be interesting:


Synonymous codon usage in bacteria.
An evaluation of measures of synonymous codon usage bias.


Regarding your second question, I don't think (and I haven't found any evidence either) that the codon usage is dependent on the neighbours.