1. Common law marriage.
Common law marriage requires a number of things to be true. However, once you meet those rules, you are legally married, for all purposes, in all states, forever. You can't just be single or "unmarried" because you change your mind.
In Texas, to have a common law marriage, you
1. must be 18 or older
2. not be married to anyone else
3. agree to be married
4. live together as if you are married
5. tell other people you are married.
Once you are legally married in a common law state, you are legally married in all states and the only way to become unmarried is to go through a very real divorce, with lawyers and courts and everything.
On the other hand, if you just lived together, but you never agreed to be married and you never told anyone else you were married, you might not have a common law marriage. If this is the case, you probably need to see an attorney ASAP to get things straightened out. (This may also change your rights with respect to your incarcerated partner, so get legal advice before you do anything.)
It sounds like you filed MFJ "with your ex" for 9 years. That's telling someone else you are married. So you are legally married to your ex. Did you get a legal court divorce? If not, you can't have a common law marriage to your current partner, because you are still married to your ex. Just because TDCJ thinks you are married, you might not be. Do they know all the facts?
You need to get to an attorney who specializes in family and marital law in Texas ASAP and figure out what your marital situation is and who you are really married to.
If you are legally married to your current partner, then here are the rest of your answers.
2. Joint tax return.
Married spouses may file a joint return as long as they agree to do so. It doesn't matter if they have been living apart all year (for whatever reason). If the spouses don't agree to file jointly, they must each file as married filing separately (MFS). Married spouses can't file as single.
3. EITC
Your spouse's lack of work does not make you ineligible for EITC. Filing jointly may even increase the EITC you are eligible for.
4. FAFSA
Not an expert here. But in a big way, it doesn't matter. You are legally married, you have to file as married, and the chips fall wherever they fall.
5. POA
The issue here is self-protection. If you want to e-file a joint return, you can "sign" electronically for both you and your spouse, and the IRS won't know whether or not your spouse agreed.
However, if you want to protect yourself from a future disagreement (suppose your spouse later claimed they did not agree to a joint return) you might want to get at least a written statement, or get your spouse to sign IRS form 2848. This is a power of attorney form for taxes only, you both have to sign. You could mail it to the IRS or at least keep it with your tax papers after you e-file, just in case your spouse later objects. He can sign next time you visit.
https://www.irs.gov/forms-pubs/about-form-2848
Also, if you file a joint return, the IRS will want to deposit your refund into a joint bank account. Do you have one, or is your account in your name only? Does your spouse have their own account? If you don't have a joint account, you may want to include form 8888 to split your refund between two bank accounts (this form is included under Special Circumstances in Turbotax.)
https://www.irs.gov/refunds/frequently-asked-questions-about-splitting-federal-income-tax-refunds
6. Back taxes.
If you find out you are still legally married to your ex, you have several years of tax returns to correct, you may have to file several amended tax returns as MFS or MFJ with your ex, since you split up but never divorced. That will likely require a tax professional. If you are legally married to your current partner, you have to file an amended return for 2021 to change from single to MFJ or MFS. But don't change any past tax returns until you get a legal determination as to marital status.
