This is one of the reasons why every frequent traveller should carry credit cards from at least two different banks and two different credit card companies (like Mastercard and Visa).
My bank recently replaced my Mastercard credit card with a Visa one, despite being Mastercard for years. I also have a Visa debit card. You don't have control over this :(
Here in Sweden many former Visa outfits have gone to Mastercard, so now it's sort of hard to find a Visa CC here. I've gone out of my way to have one Visa and one MC though.
You can just fill out a form online and get another credit card from someone else.
Yes and add to that some emergency cash.
500 USD in $100 bills is easy to carry along with your passport.
Sure. (I've been carrying around 20 * 20 Euro bills. Larger denominations seem to be scary to people who aren't used to them.)