I have read that one who knows Latin has a good command over English. Is this correct or just a myth? If it is correct, how does it work?
According to a widely-cited study on the English lexicon, close to 60% of English words are of French or Latin origin. At the very least, a knowledge of Latin would increase your comprehension of the English language, particularly when it comes words that are longer than two syllables.
The National Committee for Latin and Greek maintains that students who study Latin in high school do significantly better on their SAT scores, especially in the areas of reading and composition. (However, that could also be because Latin is not usually taught in your average public high school.)
Finally, bilingualism of any sort has all kinds of beneficial cognitive effects. A good summary of the critical literature on that topic here.