Alice just said she was the one who destroyed most everything. Killed most everyone.
But it appears there isn't any gathering of people or directly interacting with the planet that has been going on with the Praeses though. Alice seemed to only think a lot of different things about what's up here, not from the interaction of them with anyone on planet. Or any recent trips to space, whenever it was in the last thousands of years the seedlings showed up and found life. Yes, Alice didn't seem to be all that much monitoring anywhere else, but in their travels albeit limited, it didn't seem there was any interaction on Earth by the Praeses either. She only had guesses about what the Praeses are and what they want mostly. Which what they want appears mostly nothing, after all they seem to have had to create a special interface specifically for this apparently very unusual or even unheard of event of visitors. Visitors including two discontinuities, inhabitants of there embodied and transferred out of the inner realities. These inner realities are what the Praeses appear to usually only deal with. The point of whoever started all this could only have been to get them out and talking. Or whoever did this might have not at all had the Praeses in mind at all, the Praeses being Alice's supposed contact for finding out what and why, but perhaps turning out to not be the source of anything related. Which it could still be something else in the inner reality has also embodied themselves somehow. Or at the least, a way to find out who is after learning it's not the Praeses.
If it's telling the truth, which its demeanor and knowledge suggest is likely largely so, Laridia gave an answer as to what the Praeses have been doing, and it's seemingly nothing direct. When the traveling seedlings find worlds with life on them they root and start inner realities. They extrapolate on the life they find, not harvest it or something. That where they are in the inner reality, it's a more utopian version of what the planet might have become, not some attempt to make things on the planet that way. They don't appear to tell those such as Gavia and Ardent about the source planet, they're just within another reality that appears to not normally be a physical one.
Depending on how quantum they are, Church might not be permanently out. At least it's pretty apparent Sedna isn't, and Alice has certainly made a pretty quick recovery once she decided to shove some entropy away (etc). For Pate and his apparent death/murder/execution, it might have been required in the scheme of things if Church isn't permanently out. From our viewpoint it might not seem to be all that fair or just or legal, but that isn't here or now, and Alice isn't us.
If there was some sort of large-scale system of justice any longer in the post-Blink future, as there doesn't seem to be, who would be in charge? What would they be in charge of? Very possibly that would be Alice and to hear her say it, it's of everyone . We have seen her show she's not arbitrarily disposed to just killing things for no reason, even when she had at least a partially potential reason. On a more mundane level, while it might not in today's circumstances be possible to easily convict Pate of the murder of Ellie or the attempted murder of Senda, there has been coercion, battery, kidnapping, and more to the point, essentially telling Church to at the least kill Alice if not everyone. We're talking to Praeses, we don't need any of you any longer. If you were a being like Alice, any of those things might have well established Pate as far too dangerous to live, or simply as a problem that must be removed. It wouldn't though seem baseline humans in current times would be qualified to determine how legal or moral the behavior of an Alice is in a post-Blink world. Or given what she said she is, if what beings like Alice do even fit into such concepts to begin with.
Immortality, that might be horrid (especially given what we know about the chances of it and our mindset regarding its practical applicability) but on the other hand if you were immortal because you couldn't be damaged mostly and were quanta powered, you'd have some potentially limitless data storage and capacity for keeping yourself entertained. If such things were possible for a more normal person, think of somebody from say 2500 BC. All your friends and loved ones would end, and that would likely really suck at first until it just became a thing that happens that you'd have to deal with. But you'd get to see and live 4500 years of history firsthand, which although similar in events happening (or they'd become similar to you) would be different in ways depending on how you thought of it over time. Inventions, changes in culture and society and technology, political and governmental and social systems changing and modifying over time. You could do all the things Connors did on Feb 2 and a whole lot more over thousands of years once you got used to things. Yet still, as far as anyone knows, nothing like that has ever happened and isn't ever going to happen. So there's no way to ask anyone or know how you'd feel if you were. We can only guess based upon our current limited mindset and where such things aren't possible.