@Dan149
1. Even though the FSA is over-spent, it still legally counts as "coverage" that disqualifies you from making contributions to an HSA. Your contribution limit for 2022, if you had family HDHP coverage (you said prior dependents) is $608.33 for each month you were eligible. Eligibility is determined on the first day of the month, so assuming you got married on or after September 2, 2022, you are eligible to contribute $5475 to your HSA for 2022 ($608 x 9 months). If you have not contributed the full $5475, you can make an extra contribution any time from now until 4/15/2023. The tax return only cares about the total eligible amount, not when the contribution was made.
2. Because your wife's FSA ends in May, 2023 (assuming the balance is zero by the end of May) your eligibility to make HSA contributions resumes in June, 2023. Your wife would also be eligible to open an HSA in her own name since she is "covered" by a family HDHP, even though she is not the primary insured of the HDHP. The contribution limit for 2023 for a family HDHP is $7,750, or $645.83 per month for each eligible month. You would be eligible under the conventional rules to contribute for 7 months or $4520.83. If your wife has an HSA, you can split your contribution limit any way you like as long as the overall total is equal to or less than your limit.
3. If you are eligible to make HSA contributions on 12/1/2023, you can use the last month rule to contribute the full amount of $7750 for 2023. The last month rule requires you to maintain eligibility for all of 2024 as well. If you plan to use the last month rule, you can make contributions any time during the year, between 1/1/23 and 4/15/24. You don't have to wait for the FSA to end. The tax return only cares about the total eligible amount, not when it was made. (But if you have made advance contributions and then decide not to use the last month rule, you will have to remove the excess contributions before the 4/15/2024 tax filing deadline.)
4. I don't believe there is any legal way to satisfy the FSA shortfall with other funds, although that is up to the plan administrator. Your wife can try contacting the benefit administrator of the FSA and ask, the employer HR department may not know the options. However, you still have to cancel within 60 days of the life event, so even if it was allowed to pay off the balance, you have to get that done quickly. You can't pay off the FSA shortfall with HSA funds, that's clearly not allowed. If you paid it off with after-tax dollars, you would lose the tax benefit of paying medical bills with pre-tax money. If the FSA could be canceled on or before December 1, then you could use the last month rule as of 12/31/22 to make a full year contribution for 2022, with the condition that you remain eligible for all of 2023.
I suspect you will not be allowed to pay off the FSA shortfall. If your wife were to quit, the FSA would end and the employer would have to eat the shortfall, that's part of the tradeoff for the use-it-or-lose-it rule. A long as she works for the employer, I think she is stuck with the FSA until the end of the plan cycle. But it would not hurt to ask them.
