Out of curiosity:
How are the APs in the list of APs I have found sorted? Not date, that much I can tell.

And what does the second number (65) mean here:

2 65 "BOINC: ...

?

(Not the most pressing questions around, I agree.)

They're sorted by the smaller member in a pair. The number "65" is type of amicable pair. In short, first digit is how many prime factors are there in the smaller member that don't divide the larger member, second digit is how many prime factors are there in the larger member that don't divide the smaller member. You can find strict definition here: http://mathworld.wolfram.com/AmicablePair.html

Thanks for the link - interesting reading!

Has the present search recovered any unusual/remarkable/record-breaking APs yet?

The project discovered a first example of type (10,4) amicable pair:

10,4 "BOINC: Cautilus, Hooker63" 2017
60839375973463962290=2*5*13*17*41*59*73*83*109*127*241*563
75707483892585778510=2*5*503*77549*261071*743423

Finding new types of amicable pairs is a rare event.

It was also close to beat the lowest m/n ratio for known amicable pairs, but didn't break the record yet.