The bank guarantee is exactly the same as in UK. All accounts are guaranteed by the government, backed up by the ECB, to a sum of €100,000. This is the total amount of all accounts with the same bank, not individual accounts. So, if you have 100 grand in one account and 100 grand in another, only 100,000 is guaranteed. However, this is per person so if it is a joint account then each of you would be guaranteed 100,000. Of course, if all the banks in Spain and all the banks in the ECB go bust then tough, but then we'd all be fighting in the streets and living out of bins anyway. All this money that countries have been paying in to prop up the euro etc also goes into an emergency fund. If an entire country (heaven forbid) goes to the wall then the ECB emergency fund will cover the losses. As at January this year, there was 409 billion euros available in this fund and countries around the world, including UK - USA - Canada - Germany etc have promised to increase this to 1 trillion euros. Why USA? Because they are the biggest holders of secondary mortgages in the entire world.
No, you wouldn't have to pay your mortgage. Another institution, like the bank of Spain or whatever, would simply take over the accounts and your mortgage would be transferred to them. You may have heard of banks taking over others for a pound, or a euro, or whatever. These are called secondary mortgage lenders and it may already have happened to some people without them even knowing it. The downside to this is that they have to take over the debts as well. You would continue paying your mortgage to whoever the new owner, or secondary mortgage lender, is. There is no legislation, in any country, that demands mortgages must be paid if the bank goes bust. Unfortunately, this also means that if your mortgage lender goes bust, your debt is not wiped out as the secondary mortgage lender takes it over.
There is a lot of doom and gloom about this. Nobody knows what will happen, how the pound will fare, how the euro will fare. If anybody really knew they wouldn't be spending their time answering questions on chat sites, they would be out earning an absolute fortune on the financial markets.