If your visa is based on a marriage, and your spouse dies, you can remain in Thailand until the end of your extension. After that you either need to apply for an extension based on a new reason, or leave Thailand.
firstly unless you applied for a visa before you travelled you don't have any visa but you are stamped in for 60 days Visa Exempt. Now yes this is enough time to convert to a Non O. However there are reports you might not be able to get a bank account to park your money. Do you have a bank account?