Should I kill any strings to this relationship, because this relationship just came out of no where? It wasn't planned, or maybe it was not sent from God and it is not meant to be and just talk to each other normally? By normally I mean we remain good friends but we know there is something between us.
God may have sent her in your path to bring you closer to the Lord; but I still think you should just keep the friendship and do not go further. Remember "to everything there is a season, a time for every purpose under heaven" (Eccl 3:1) and that this is not the right time for you to start such a relationship.
There are also many factors you need to consider in this particular case since she is older than you:
First: the level of maturity of both of you. I am sure you feel mature enough to make decisions; but remember that females mature faster than males and if you are in your late teens, early twenties, and she is two and half years older than you, most probably she is way more mature than you. What startles me though, is your parentsí reaction and how they are happy about the matter and already announcing it when they have never met the girl.
Second: women tend to age faster than men, so the difference in age will affect your relationship later on.
Third: you already anticipate resistance from her parents. Think of the position you will put her in when she has to defend her choice and convince her parents to accept a nonstandard situation.
Do not rush into any commitment nor plans for commitment. It is too early for you.