1: Since EMV uses dynamic CVVs, a CVV of a recorded transaction is useless, since its spent. Thus they lack the complete info to create a (functioning) magnetic stripe card. However, doing a fake transaction might give a working magstripe card. But that magstripe card will only work a single time, and not work after the cardholder does any legit transaction, and then the bank will immediately detect the out-of-order iCVVs and thus block the card.
Also the frauster needs to be able to predict certain random numbers, which in some cases might be predictable due to terminals lacking good RNGs.
2: Different CVVs are used for different purposes, eg one CVV for CNP transactions, one CVV for magstripe transactions, one dynamic CVV using keyA for Contact chip transactions, Another dynamic CVV using keyB for RFID transactions.
This allows the bank to differentiate by different transaction types.
All POS transactions are recorded differently from all online transactions, HOWEVER:
Some webstores process their transactions as POS transactions. That causes the system to accept the transaction anyways.
Some retailers also do not require CVV, sometimes this is retailers that do not put a authorization hold on the account when first setting up a stored card to account, and since its prohibited to store CVV in ANY WAY, they don't ask for it since they have no means to verify it without charging the card. They allow you to set up the stored card.
Most reputable companies instead ask for CVV when storing the card, and then charge like 1$ to the card to check if the card does actually work and then adds this amount to your account on-site. This does however put off some customers.