If we have already registered with a specific team for snackdown preeliminators and now want to register with a different team for the snackdown mirror is this is possible or we are bound to use the same team?
you can use your old team or you can create new team,it is up to you.Both are possible.
will this contest affect my rating?
no it will not affect the rating
then only three monthly contest(long challenge,cook off,lunch time) affect my rating?
yes only those three affect your rating and sometimes some external contests will be rated .