I lost cards many times. Never been asked to pay a fee to get new card. No forms to fill out either. You just call them, tell them you need new card and they send it.
But try losing your card overseas and see how you feel then... Especially if you have to put a stop on your card... Slow and very painful...
Unless you have a spare you'll be asking a friend to use Western Union for bridge finance.
Depends on the card. With Amex or Diners Club it’s not a problem.