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It is the sum of the monthly contributions (1/12 for each eligible month) but as long as the taxpayer is age 55 by the end of the year, then the person will be allowed the full catch up if the taxpayer is in a HDHP for each of 12 months, even for the months before he or she actually turned 55. In other words, for 2020 someone with single coverage and 55 or over by year end, the allowed monthly contribution is $379.16 (1/12 of ($3,550 + 1000)). For 2020 with family coverage and over 55 by year end, the monthly amount is $675 (1/12 of ($7,100 + $1,000)) for each month of eligibility. In both of your examples the TP is eligible for all 12 months, has family HDHP, and is 55 by year, so the contribution allowed will be the same = $8,100.

If her motive is profit, my answer would be yes. I successfully got a "no change" on a partnership audit, because of years of regular losses. They partners ARE in it for a profit motive. They're just really bad business-people. That first part IS in the IRS regs, and the second part is NOT. I think the main part of my argument was simply that incompetence does not preclude profit motive, and was able to show that motive as well as (futile) steps taken to improve. That's a long-winded way of stating the simple fact that several years of losses does not, prima facie, constitute lack of profit motive. If, however, she still skates professionally "because she loves it" and would do so even if never paid, then you have a hobby. If she is working on her standing to open a school, then you're in a gray area; does she have profit motive for what she is doing currently?