UK261 doesn't apply as the flight was on United, a US carrier, from the US. Had it been the return or on a UK or EU airline, UK261 would apply.
If you use the credits on the Gold fairly regularly I would keep it just for the earning potential. Most of my family's spending is on groceries and restaurants, both 4x categories on the Gold and 1x on the Plat.
If it's on her boarding pass she will be allowed through. There are a defined number of places in Precheck lanes for each airport each day. If there are fewer precheck enrolled passengers than there are slots available there is an algorithm run to determine who else gets the checkmark. Contributing factors are age, travel history, travel party, background checks that we know of. My mother is 63, works in a school and goes through a background check every year, she's had a FF account going back to 1982 with Northwest Airlines and flies a couple times a year. She gets Pre about half the time flying between MSP and MDW.
I enrolled in Pre in 2019 and it took 4 days. I applied for Global Entry in March and am still waiting for my conditional approval, then once I have that I have to find a location to interview. The nearest interview location to me is 90 minutes, the nearest that has bookable appointments right now is 4.5 hours. It may be cheaper and easier for me to fly somewhere else just for the interview, then fly home.
Pre lowered price in November of '22 to $78 for initial enrollment, $70 for renewals stayed the same.
I'm going to rant against Clear for a minute, but may be a hypocrite next week. In many locations, Clear takes their customers and lets them cut the line in front of other passengers. I feel this is wrong and should not be allowed. This is allowing someone to pay a private company to skip to the front of a government operated line. In MSP in 2021, it would have been faster for me to go through the general security line rather than Pre because no one without Clear was allowed into the Pre checkpoint if there was anyone from the Clear line waiting. This has been solved in many locations, including MCO by having a separate checkpoint for Clear customers, which I'm okay with. I got a three month trial offer via email. I've got a flight next week, maybe one in the middle of June and probably one over 4th of July. I'm undecided if I'm going to go through with it, but I might.