First of all, when either spouse has an HDHP, both spouses are considered to have an HDHP and both spouses are eligible to contribute to their own HSA. The limit is $6900 per person for 2018, but the combined limit for spouses is also $6900. Over age 55, you are eligible for an additional $1000 catch-up contribution. If you enrolled in Medicare in September, then your maximum contribution for 2018 would be $7900/12 x 8 months = $5925.
The fact that you made some of the contribution after September does not actually matter. Turbotax should not flag this as an excess contribution. In fact, you should be eligible to contribute an additional $2875 and take a tax deduction, if you do it before April 15 and if you inform the plan trustee that you are making a directed contribution toward your 2018 limit.
Once you own an HSA, you can spend the balance for qualified medical care for yourself, a spouse or a dependent, and the money is tax-free, even if you are no longer eligible to make new contributions. At age 65 or older, you can also withdraw the money for any reason and pay regular income tax but without the additional penalty for non-qualified use (similar to a regular IRA).
An HSA is owned only by one person, like an IRA, there are no joint HSAs. Your spouse is eligible to open an HSA in her name if she wants, there are many private banks that offer this, it does not have to be through her employer. She can make contributions directed to 2018 if they are made before April 15 and she informs the bank of her intentions, her contribution limit would be $6900 minus whatever you contributed**. Her contribution limit for 2019 would be $7000 (she is eligible even though you are not, as long as she is enrolled in qualifying HDHP.)
**Her contribution limit is actually a tad higher than that due to the effect of your $1000 catch-up provision, but I don't want to go through the math right now. If you really want to contribute every possible penny, I will help you figure out the amount.
