1) Yes. It is the income limit that can make the filing mandatory. However, in your case, I would still recommend that you file your return and mark your wife as deceased and enter her date of death into the IRS data base. If her SSN is not already blocked, that action should guarantee that nobody else can use her number in the future.
2) You only get the MFJ option for the tax year in which the death occurs. The following year, without any dependent child, you would file as SINGLE.
3) I am confused by talk of "refund" since you did not mention having income that would have generated withholdings or situations which would indicated any tax credit. Lack of adequate inputs often leads to incorrect outputs. But if someone would have a refund, from a W-2 for example, then they should file to get their refund. And don't wait. File for each year, and file on time. Forget about this 3-year stuff. Just because you might be able to get away with doing that does not mean that you should do that. April 15, 2019 is the due date to file your return for tax-year 2018.