1. If you download full form 1040, it will have additional "schedules", or tax forms. Depending on other income received, aside from the SS benefits, you may need some of these form or none.
2. You wrote, "I have to start filing my US taxes". Have you and your husband filed them previously or this is the first time? If you had filed in the past, then find the previous year returns and you will figure out which forms are applicable to you.
3. You did not provide information on the amount of benefits and your other income. It is quite possible that Social Security benefits received are fully or partially non-taxable. You will use worksheets enclosed with the form to figure out taxable amount.
4. As far as filing status, yes, you can continue filing as married filing jointly for two years after the date or death of your spouse.