Jews, A question about Noachides?

I was just wondering where the "Noachide" came from. My previous understanding was that the Noachide and the 7 Noachide Laws where in reference to all non-jews. However in my recent research I have found that the "Noachide" seems to have come about as a sort of preventative measure against infiltrators in a time of great persecution, and that the 7 Noachide laws were derived through Kabalah (sorry if spelt wrong). Can a Noachide (or gentile whichever you prefer) follow any of the 613 mitzvot? I have been looking into them and researching them and it seems that some of these are directed straight towards Gentiles and Proselytes. Obviously a noachide can't keep all as some are specifically for jews, some for women, some for priests etc. I only ask becuase i have heard it said many times before that a Noachide can not keep any of the mitzvot and can only follow the 7 laws, but that doesn't make sense to me becuase as mentioned before some are for gentiles, or am i just being ignorant?