if a transfer call was doubled, the opener completes the transfer only with fit3 (with fit4 bid normally 3x); pass from opener means doubleton and then redouble from responder is RE-TRANSFER. after re-transfer, responder may continue with NON-FORCING (but INV) bids on 3 level. redouble from opener means TO play, no fit in responder suit and usually 5 cards there (yes, even in a major, 5 cards)

after a double to 2S (which is bal inv or clubs), pas=minimal, no spade stopper; 2NT=minimal+spade stopper; redouble=to play, 5 spades

when 1minor takeout double is left for penalty, tend to believe opponents. redouble from opener is SOS, usually with a semi-balanced hand. it is in fact mandatory with a balanced hand since responder cannot act with a weak hand even with a long suit.