Bridge: Usage of the stop card
The answer to your first question is that you should use it either for all skip bids, or for no skip bid. Using it only for some skip bids but not for others could result in a director call and a procedural penalty against you for intentionally transmitting unauthorized information to your partner.

As to your second question: option 1 is correct under the jurisdiction of the ACBL (ie essentially all games in the US and Canada), while option 2 is correct under the jurisdiction of the WBF (essentially all other games).