Before you get too far looking into the HSA, you definitely want to be sure that your health plan is an HSA-eligible High Deductible Health Plan (HDHP). There are minimum deductible amounts that your health plan needs to meet to be an HDHP, but there are also maximum deductible amounts. The maximum family deductible amount for 2021 is $14,000, and the deductibles you have listed seem to be above that maximum. There are some complicated rules regarding this, so I suggest that you ask your health insurance company directly whether or not your plan is HSA-eligible. If not, you may want to consider changing plans during your next enrollment period.
Finding an HSA
Banks are the most common places to offer HSAs, but there are also investment companies that offer them. See this answer for things to consider when looking for an HSA.
Funding the HSA
HSA contributions can happen in two ways: The contribution can be sent in by the employer, or they can sent in directly by the account holder. If the employer sends in the HSA contribution (even if the money is taken out of a paycheck through payroll deduction), that amount is taken off of the employee's W-2 at the end of the year. As a result, the amount is automatically deducted from the employee's income for the income tax. This method also avoids payroll tax on the amount.
If the account holder sends in their own contribution, then he takes the HSA deduction on his 1040. This method gives the same income tax deduction as the first method, but no payroll tax savings.
Either way, the account holder needs to file Form 8889 along with his tax return, which will calculate the amount of the deduction and ensure that no limits have been reached. It will also calculate any penalties if any of the rules have been broken.
Your contributions do not need to be made monthly or on any sort of schedule. You can put money in whenever you like, up to your annual contribution limit.
Reimbursements for medical expenses
The rule is that any medical expenses that are incurred before the HSA is established are not qualified to be paid for out of the HSA. So if you set one up in November 2021, you cannot use it to pay for expenses that were incurred July 2021.
However, those expenses that are not reimbursed by your HSA or your health insurance could potentially be deducted by taking the Health Expense Deduction as part of your Itemized Deductions on Schedule A.
For more information about the HSA, read IRS Publication 969.