I'll address three issues here:

[Spoilers follow ... ]

1. Demerzel tells Sareth she's the last surviving robot, that once upon a time robots were bound to follow three laws which makes them bound to prevent any harm from befalling a human, by action or inaction (actually, just the first law of Asimov's Three Laws) but that changed and now she's bound by only one law, to "serve Empire".

Ok, but is Demerzel Telling Sareth the truth?  Is she bound by any robotic law to never lie to any human?  Or never lie to Day's betrothed?  Not likely.  And why did she mention the three laws to Sareth, and then only recite to her the first law?  Was that just inexact writing, or is there some meaning in that omission?  And is Demerzel telling the truth about being the last surviving humanoid robot, aka android?  (And, while we're at it, what happened to Asimov's Zeroth Law?)

2.  The Cleons had quite a night.  Day had Demerzel kill Sareth's family.  She understandably hates him.  Day and Demerzel know this, so why are they going ahead with the marriage?  And Sareth beginning to seduce Dawn is a risky and exciting venture indeed.  I don't see how they'll be able to hide that from Demerzel.  Also notable is Brother Constant conveying the holographic Harry in the meeting with the Cleonic clones and Demerzel in a very strong scene -- actually, any scene with the Cleonic clonic triumvirate and Demerzel is good to see, let alone one with any version of Hari.

3. But speaking of Hari -- it looks like he's also alive in the flesh, with his head above water, just as I said I thought was likely the case last week.  And now Salvor has joined him?  Well, not exactly, her face is down in the water, but if Hari survived why can't she?   On the other hand, this episode is entitled "A Necessary Death," and whose death is that?  Sareth's family? Not likely, especially since that happened off-camera.

Lots of information and lots of questions, which is why I much enjoyed this episode.

See also Foundation 2.1: Once Again, A Tale of Two Stories ... 2.2: Major Players ... 2.3: Bel Riose and Hari ... 2.5: The Original Cleon and the Robot ... 2.6: Hari and Evita

And see also Foundation 1.1-2: Mathematician, Man of the People, and Cleon's Clones ... Foundation 1.3: Clonal Science Fiction, Hari Seldon as V. I. Lenin ... Foundation 1.4: Slow Hand, Long Half-Life, Flipped Coin ... Foundation 1.5: What We Learned in that Final Scene ... Foundation 1.6: Folded Variations ... Foundation 1.7: Alternate History/Future ... Foundation 1.8: Divergences and Convergences ... Foundation 1.9: Vindication and Questions ... Foundation Season 1 Finale: Right Up There