Should I use Come or Go?

I will come with you. Can I come too?

Both are legitimate. You can use the "go" as well, but I prefer "come". The intonation when you are speaking can influence the meaning, as well.

In your sentences either works.

If the statement applies to accompanying a person who is going somewhere , then go would be more apt.

Comparing "Go" and "Come" in a 'directional " sense we have "Go TO the store---" , "Come HERE as soon as possible