Does a countries GDP reflect the total Income of the entire entities in the country?

Well to clarify first Gross Domestic Product is the total market value of goods and services manufactured in a certain country. Referring to your example. If country A has a GDP of 10mn$ then ceteris paribus the total income the firms can earn together cannot exceed 10 mn. However in the real world we have to account for changes i.e not all the goods might be sold in country A and if trade takes place a certain good manufactured in country A with a market value of lets say 20$ can be priced at 25$ in country B. So yes in that case the total income of the combined 10 companies can be more than 10 mn$ for the same period.