Yes you can eat them... not sure I'd want to though. Bit early to be expecting decent size carrots if you only sowed in April. Carrots, and parsnips, prefer a light sandy soil and need a very fine tilth, and stones, even small ones, will cause the root to bifurcate. What have you been feeding them on and why?

Carrots don't need feeding. You simply plant or sow them into well-prepared ground and let them grow.

In fact the 'feed' will have contributed to the luxuriant green top growth!