I hope you all enjoy this series of Videos on Esper Mentor in the latest Power 9 Challenge on MTGO
Game 1 Turn 2: Blind-naming Force of Will is interesting. You didn't have other action to win that turn and you were very likely to hit more Therapies with double Bazaar active next turn and a couple of big Dredgers available. I would lean towards Time Walk, Containment Priest, Monastery Mentor, or Preordain there (having seen Library and a discard of a blue fetch). With two Therapies there is at least a case to name Force (and push through the second Therapy on a real card) but I think when the Therapy resolves that's a reasonable indication that there's not a critical card being protected (specifically because Force is such a common card to name)
For the Game 1 reanimation sequence, I think nailing Black Lotus and his dual land is probably better than hitting both his lands (his perspective makes that clear, but I think it's true in general). I didn't track your Therapies closely enough but you might have been able to nail all his permanents by sacrificing the Archon to a Therapy and bringing it back, which I think would be the best line. I think Ruric Thar is unusually weak because he's running Swords to Plowshares, which you should be able to deduce because you saw Monastery Mentor.
Game 2 Turn 2: He had only 3 cards and 2 lands in play, so I'm also iffy on the Monastery Mentor name here. I think you're far enough ahead that you should just name Ravenous Trap. If you're worried about Mentor I think Gush might be the correct card to name as land, Mentor, Gush is the most likely hand to beat you from that point and Gush is valuable without Mentor but Mentor is not valuable without Gush or Black Lotus (even if one of the cards is a Mox he would have to topdeck the final ingredient in a four-card exact lineup just to cast a cantrip). It was reasonable to identify Mentor as the biggest threat, but I don't think naming Mentor is the highest-value way to address that threat.