These are great questions and to be honest, we don’t have all the answers yet. But we want to find the best solutions over the next months with the help of the community. That is why we launched the alpha program! 
If you lose your card bank card, you should not have to wait day for a new one before you can get money out. We will not have our own branches but will find other ways of solving the problem (there are a few good examples above). While we are waiting to become a bank, we stress that you should ALWAYS have a backup card with you in case the Mondo card is not working (it is an Alpha and we are still fixing bugs).
Today, if you lose both card AND phone, you should either email us at help@getmondo.co.uk or call the number at the back of the card (remember to write it down before you lose the card 
). We are also soon adding TouchID check before topping up to make sure it is the only you who can top up your account.