I want to know if I can alternate between Married Filing Single and Married Filing Jointly. We changed from MFJ to MFS several years ago. Can we change back to MFJ?

Yes, you can. 

Yes.  Each tax year is separate.

To begin a new joint return on TurboTax:

You will not be able to merge two previous TT account to start your new joint return.  You can transfer ONE of your 2019 returns into a new return, so choose the most complicated one.  The other spouse’s information needs to be entered manually.

When you enter your own information in My Info, you have to answer the question "Were you married?"  If you click the button for Married, then a drop down will appear that asks, "Do you want to file this return together with your spouse?"  Then you choose yes to file a joint return.  You would then enter your spouse's information into My Info.  Whenever you are entering income information there should then be a spot for you and for your spouse's income information.  Income screens will have spots with each spouse’s name—be careful to enter under the correct names.

If you were legally married at the end of 2020 your filing choices are married filing jointly or married filing separately.

Married Filing Jointly is usually better, even if one spouse had little or no income. When you file a joint return, you and your spouse will get the married filing jointly standard deduction of $24,800 (+$1300 for each spouse 65 or older)  You are eligible for more credits including education credits, earned income credit, child and dependent care credit, and a larger income limit to receive the child tax credit.

If you choose to file married filing separately, both spouses have to file the same way—either you both itemize or you both use standard deduction. Your tax rate will be higher than on a joint return. Some of the special rules for filing separately include: you cannot get earned income credit, education credits, adoption credits, or deductions for student loan interest. A higher percent of your Social Security benefits may be taxable. Your limit for SALT (state and local taxes and sales tax) will be only $5000 per spouse. In many cases you will not be able to take the child and dependent care credit. The amount you can contribute to a retirement account will be affected. If you live in a community property state, you will be required to provide additional information regarding your spouse’s income. ( Community property states:  AZ, CA, ID, LA, NV, NM, TX, WA, WI)

If  you are using online TurboTax to prepare your returns, you will need to prepare two separate returns and pay twice.

https://ttlc.intuit.com/questions/1894449-married-filing-jointly-vs-married-filing-separately

https://ttlc.intuit.com/questions/1901162-married-filing-separately-in-community-property-states

https://ttlc.intuit.com/questions/1894449-is-it-better-for-a-married-couple-to-file-jointly-or-separately

If you are going to amend a prior tax return-  You can amend a return to change from married filling separate to married filing joint but not from married filing joint to married filing separate unless you do so prior to the original filling deadline without extensions. So, once you file a joint return you can not change it to a separate return if the filing deadline has already passed.

Regarding the a new filing, for the current year. you can choose the status that best suits your needs. 

Deciding which status to use

The best way to find out if you should file jointly or separately with your spouse is to prepare the tax return both ways. Double check your calculations and then look at the net refund or balance due from each method. If you use TurboTax to prepare your return, we’ll do the calculation for you, and recommend the filing status that gives you the biggest tax savings.