On the subject of Monastery Mentor: This is my theory-crafting, and I'm not the best player, so take it for what it's worth.

From a deckbuilding perspective, compared to some of the recent Entreat builds, a deck with 3 Mentors is generally sacrificing one Counterspell + one Terminus. Cutting a Terminus makes some sense, as you don't want to sweep away your Mentor and the Monk tokens do a decent job of creating board stalls in some situations, acting like a pseudo Moat. So you're down a piece of countermagic in the main, but in the sideboard, you have some free slots since you don't have any Mentors in the side. And because you have a threat instead of more defensive measures in the main deck, it incentivizes you to play a little more aggressively in some situations. But it also allows you to not care about 'wasting' your win condition, since you have multiple (setting Jace & Snapcaster beatdowns aside for the moment).

I suppose I view Mentor as serving a few different functions:

1. As a late-game play when the game is under control, it is a win condition.
2. As an early or mid-game play when the game is unstable, it can be a bridge to the late game.
3. As an early or mid-game play when the game is potentially quiet, it can be a win condition.

#1 is pretty similar to Entreat. Mentor is more fragile and a bit slower in these situations, but hopefully by this time the difference isn't substantial. But Mentor enables #2 and especially #3 in a way that Entreat doesn't. By running multiple maindeck Mentors, you can run one out without too much fear of it being killed in situations where it might win the game. Sometimes it will die right away or after making only a single monk, and hopefully buy you time to find a Terminus / Jace / etc. But other times, the opponent just won't have the answer and an early Mentor will win you the game.

Brian Braun-Duin wrote an article for TCGplayer a while ago with some thoughts on Mentor that I think I agree with:

I don't view cards like Mentor, Jace, Blood Moon or even Counterbalance as win conditions. I view them simply as means to an end. I see people too often playing scared to drop their Counterbalance into an answer or play their Mentor out unprotected on turn three, but those are the plays you have to make. I view these cards as expendable and often jam them as early as I can and force them (sometimes literally Force them) to have an answer. Yeah, sometimes they have the Spell Pierce for your Counterbalance or the Daze for your Monastery Mentor. In that case, you get to just keep playing the game. But when they don't have those cards, well, they're probably just dead.

When you play the game this way, it puts a lot of pressure on them to keep up. Normally, Miracles is playing from behind and trying to leverage Sensei's Divining Top at the right times to wrest control of the game before it's too late. Well, I find that it often ends up being too late when you're facing down the kinds of threats people are playing today, like True-Name Nemesis, Liliana of the Veil or Leovold, Emissary of Trest.

With the Mentor version, you have a quick way to turn the corner and sometimes you also get to force them to play from behind, which is not where Delver decks traditionally thrive. When they are trying to play catch-up and are spending their turns answering your threats, you are in the driver seat. Now that's what I call control.

...

Playing with these kinds of powerful game-ending effects and playing them proactively and without fear is how Miracles wins a lot of these games. As it turns out, Mentor is a more powerful threat than almost anything your opponent can be doing. If they don't have an answer to a Mentor, you'll outrace Delver or Death and Taxes or whatever creature deck they are presenting. If they do, then maybe the turn they spent killing your Mentor allows you to successfully stick a Jace the next turn.
I think some of the assessment has changed since the Top ban (you can't Top on upkeep and replay Top to get a one-mana Monk every turn, so it's a little harder to be as aggressive with Mentor), and I think that without Counterbalance it makes sense to be a little more cautious running out an early Mentor since it's harder to protect, but I think the general principles still apply: Mentor allows us to quickly become proactive, force the opponent to 'have it', and if nothing else buy time to find a Terminus / Jace / etc.