He double-checks, answering a few prayers and updating the list again while he's at it.
"Yeah, I can do that."
Then he offers Kaylo the choice of a sparkly teleport to the library, answers some prayers, has a quick peek through the library for relevant books, and marks the ones he finds with tiny little fluffy creatures clinging to the tops of their spines. The creatures are brightly coloured, and look sort of like extremely small Snitch-winged bird-feeted pompoms.
Kaylo goes ahead and skips the lift trip, uses conventional library spells to get ahold of the books, picks up a critter, snorts, puts it down, and starts looking through the selection. Eventually he has one picked out. It requires a diagram. "Can I get a stick of summoning chalk? I don't have my own at the moment."
A stick of summoning chalk appears! The library creatures form a tidy little pile on an out-of-the-way corner of Kaylo's table once he has collected all the books that have one attached.
The library creatures disperse. Teah watches Kaylo, listens to Leekath, and grants assorted prayers.
If Leekath were to go through with her plan, the result would be: a sleeping Teah-body, a purple floor.
"Purple floor would be funny, but yeah, nah." The tag on Leekath's bottle changes to I am harmless but ineffective. "Seems like this kind of thing actually works, though, which could come in handy if we wanted to try anything else..."
Teah keeps half an eye on Kaylo while he goes and answers more prayers.
It's mildly interesting to read 'over his shoulder', but it'd be a lot more interesting if Teah could spare the attention to look up what all the bits and pieces mean. He's busy, though. He is always, always busy.
He deals with the experiments much the same way he did at home - ignore a lot of people who are praying only to see if it works or find out what he can do, treat meaningful prayers that happen to be occurring in an experimental context just the way he would outside of one, and occasionally give out whimsical results or hurried, nondeliberately-cryptic verbal responses.
Hey, stymieing experimenters is informative in its own way. It informs them that he has better things to do, and an offbeat sense of humour. If he very seriously answered every single experimental prayer, that would just create an expectation that he answers experimental prayers seriously, which would ultimately turn out to be false. (He's been through this logic already back home; in fact he suspects he's been through it more times than he remembers.)
He eradicates every disease in the world that lights can't touch, and plenty that they can. He interferes extensively in Ryganaav as Kindness, mostly to save lives, in varyingly subtle ways. He's so charmed by the library creatures that he keeps including some whenever they are remotely justified, and soon many people have helpful little flocks of fluffy bird-feeted Snitchlings ranging in size from 'large pea' to 'small grape', with the ability to pick up and carry objects hundreds or thousands of times their own weight. It's tremendously cute. Speaking of tremendously cute, the world's first magical puppy kicks off a bit of a fad, and a couple of enterprising individuals ask him for an assortment of interesting dogs capable of growing up and making more dogs. He provides.
He checks in with old petitioners every so often, but happily, most of them don't seem to need him for anything.
When Kaylo gets his attention, he finishes a few prayers he had his eye on and then says, "Cool! How's it work? Want me to update the book to see if you can see it?"