When putting both in a sentence?
My understanding as a school child was, it should alway be 'I' when you're talking about yourself and someone but somewhere along the line, I picked up a new rule and I have no idea if it's correct or not 
Take these sentences...
"Are you taking me and Sarah in your car?" I think that's correct because if I remove Sarah from the sentence/question it reads "are you taking me in your car?"
If the sentence was "are you taking Sarah and I in your car?" and you removed Sarah from the sentence, it would read "are you taking I in your car?" which is obviously wrong.
"Sarah and I are going in your car" is correct (according to my rule
) and "me and Sarah are going in your car" is incorrect because, again, if Sarah is removed from the sentences, they would read "I am going in your car" or "me is going in your car"
Am I right, nearly right, a little bit right or way off the mark? 