What is the difference between "расскажите мне" and "скажите мне"?
Both mean, tell me!?
And also may I remove мне in both cases?
Расскажите - implies a story, some description. Скажите - just say, tell.
Скажи ему, что ты его любишь = Tell him that you love him. Расскажи ему, КАК ты его любишь (in the sense 'describe your love') = Tell him how (in what way) you love him.
As for мне - it can be omitted if the meaning is clear from the context (regardless of the verb used). Рас\скажи мне, как ты меня любишь. - Рас\скажи, как ты меня любишь. (the latter is possible if it's a dialogue and 'to me' is implied, or if you want a group of people to hear the story).
The difference between these verbs is pretty much the same as between racontre and dire in French. In English both sentences mean 'tell me', and yes you can drop "мне" in both cases.
The main difference is the length/depth of the answer you are trying to get out of someone. "Расскажи/те" implies there is a story to tell. For example you want to know how someone have spent their vacation or how they got a job that you're interested in. You are expecting at least a couple of minutes of the story with at least some details.
Ну, рассказывай, как слетал, что видел.
"Скажи/те" implies there is some really short answer to be given, one, max two sentences. Sometimes it's used when the question is really rhetorical and you don't expect an answer (of any substance).
Скажи, вот какого чёрта тебя туда понесло? Дома не сиделось? Просто скажите мне во сколько мне лучше подъехать и я там буду.
Often "Не подскажешь/подскажете?" is used, especially when asking for directions, though it literally means "could you give me a hint?"