You can always file a return, even if you don't owe any money. If you don't file, and based on 1099 information reporting and other sources, IRS determines you may owe some tax, they will create a substitute return and open an assessment for that amount. If you are entitled to a tax refund or tax credits, you also can't claim these unless you file. I'd at least prepare a draft return to see if it's worth filing.
I am sorry to learn of your loss. The Social Security Administration should have been informed of your wife's passing, and her checks should have stopped. If she received an excess check in April, then that should be repaid. Check with the Social Security office to be sure that all is OK with her account.
Because you say that your are both "green card holders", your status would that of a RESIDENT Alien for U.S tax purposes. Because your wife passed in 2018, then you would file with status of Married Filing Jointly (MFJ)--if you need to file. You would include all of your 2018 income and as well as your wife's income for the year. The gross income threshold for filing for a 2018 MFJ tax return (both over age 65), is $25,300 based on income which is not exempt from tax. So with the income that you indicate (and assuming that you stated all of your combined income), then you are well below the filing requirement. It does not appear that you have a requirement to file. However, you can file if you want to file. Because I don't know how well the IRS connects with Social Security, some of my friends tell me that filing the return, and marking your spouse as deceased, might be a good practice to help stop future fraud attempts. You would not owe any tax money for 2018 with the income that you stated.
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.
It is also possible you may use the "Head of Household" or "Widow/Widower" filing status in later years rather than Single. There are certain requirements (like qualifying dependent) which must be met for you to qualify to use these statuses, however.
What you're doing here is really dangerous for you, because as the above demonstrated, tax rules can get complicated and many circumstances you didn't realize are relevant can change your tax benefits or liability significantly. Another example is the "kids who do not live with you", but if you're filing jointly with your spouse and they lived with them, then they do live with you! And of course there is the health insurance individual mandate. And then what about foreign income?
Also, have you or your spouse filed in previous years? The final deadline to file or amend for tax year 2015 is coming up April 15, 2019. Amending means things such as claiming a tax credit that was omitted on the original return or changing the filing status from filing separately to filing jointly, which can only be done until that final date.
I understand that you're still dealing with the death and all, and probably would rather just skip the taxes this year if at all possible (or rather, defer doing them until next year). However, this community is not the correct place to get advice on what you should do or are required to do, rather it is a place to ask general questions on the tax law and procedures and get opinions on what might be appropriate. I've said earlier, and I'll say again, you should get professional advice or at least go through the tax software interview process to get the best picture possible about what filing taxes would mean for you and if you owe anything. If you don't understand something in there, then ask a specific question about that topic, not a generalized question like "AGI is all that matters to determine if I need to file" which is very open-ended.
Unless you change your family situation, you will file as "Single" next year and for years moving forward. Other filing status will not apply to you. However, you should revisit this conclusion if your family situation changes such that you pick up a future dependent who can be classified as a qualifying child or a qualifying relative. Here is an IRS link that can assist you for filing status: https://www.irs.gov/help/ita/what-is-my-filing-status
Yes, the income limit changes when Single. This year, the Single, over age 65, income number for filing is $13,600. This is basically just the Standard Deduction number. At that income point, your Social Security income will not be taxable and will thus not count toward the income number. Here is the link to the IRS that can provide additional assistance: https://www.irs.gov/help/ita/do-i-need-to-file-a-tax-return
Here is a more complete treatment of filing requirements. However, your description of your situation does not appear to include these cases.