Below are the current Railroad Commission maps for the two areas of Gaines County that are described in the leases you posted.
In Section 372 the map shows two vertical wells, each in an 80-acre unit that covered half of that south half of Section 372. The well marked #3 (called the Peck “B” #3) was drilled in 2002. Over the next five years, it made a total of about 93,000 barrels of oil and a little gas. The last production was shown in 2007 but the map doesn’t show that it has been plugged and abandoned.
The well that’s near the south end of the section, marked 1X (called the Peck “A” 1X), was drilled in 2013 but it didn’t show any production until 2016 and from then until 2022 when it was shut-in it only made a total of 130 barrels of oil. Since that second well was drilled after your mother signed that lease I guess it’s possible that 80-acre unit could have included her mineral interest. Although neither of those wells are producing, a company called Phillips Operating LLC is still shown as the lease operator.
On the second map covering Section 3, Block C-35 shows two vertical wells in the southwest quarter of that section but both were plugged as dry holes. The well furthest south appears to be very old, probably drilled sometime in the 1960s, but the other one, marked #1 37300, was drilled by Griffin Petroleum, the company your mother leased to. RRC’s records show that well, called the Lost Draw, was plugged February 20, 2011, less than a month after your mother signed the lease with Griffin. The plat showing the location of that well is attached below the RRC map of that section.
On your other questions, I don’t see how your mother might have “done anything harmful by signing these leases,” unless for some reason you think she didn’t inherit that mineral interest previously held by your father after he died.
Determining the amount of mineral interest your father owned in those two sections would require some more research in the Gaines County deed records. Since you already know how to use TexasFile, if the description in the leases doesn’t give a deed reference that will get you into the chain of title, try searching your father’s name (or the names of others he might have inherited or otherwise acquired that interest from) in the grantor/grantee indexes trying to find the deeds where he gained title to that interest.
Regarding the current status of those leases, the one with Griffin Petroleum was only for a one-year term and should definitely be expired if that well was plugged as a dry hole. I expect the lease with Rio Rancho in Section 372 is also expired but since the wells in that half section aren’t shown as being plugged you might try checking with Phillips Operating on the current status of that lease.