99.9% of people use way way way to much rosin. You should never ever have more than a extremly light dusting of very fine rosin particles after say 1 hour of vigorous playing.
No, the frog does not need more rosin than the tip or middle, unless of course you want a cloud of dust everytime you attack.
In addition, if you have nice quality hair on your bow and you have you bow rehaired enough, then rosin is not needed to prevent sliding, it simply increases the life of the hair, while giving a more connected sound. If you can slide your fingernail on the hair and it turns white then you have to much rosin.
When to much rosin has been applied, the hair is not longer contacting the string, it is simply skating around on tiny rosin beads... hence the gritty sound that many people have, due simply to overuse of rosin