Some Immigration Offices require that the bank account is in your name only but if they do accept a joint account then the financial requirement (800k for retirement) will double
Yes, better to enter on a retirement visa (usually Non-O, 90 day stamp) as this will make it easier to open a bank account which will be needed to get your 12 month extension
You will get a 60 day Visa Exempt stamp on entry which can be extensed once for a further 30 days (1`900B). You then have to leave but can re-enter to do the same again. If you tried this border-bounce a second time then you will most likely get grilled by Immigration at least and possibly denied entry.
You will need a police report for your lost passport to enable you to get your stamps transferred to the new passport and, probably, to enter using the new passport?