Played a match on Small vs Normal AI. I deliberately skipped the tutorial, because your first question is whether the capture mechanic is clear without instructions — so here is that answer honestly, plus one thing that looks like a bug.
The bug first: I set FIRST MOVE to "You — You place the opening dot", started the match, and the header said "AI to move". The AI placed the opening dot and I moved second. Either the setting is not being applied or the label is inverted.
On your question 1 — no, not from the board alone. Once the tutorial is skipped there is nothing on the play screen that says what a capture is, how large an enclosure has to be, or that captured dots are what score. I placed dots next to the AI's and nothing told me whether I was building toward anything. The tutorial is carrying the entire rules explanation, so "skip" is effectively "play without knowing the win condition". A one-line hint on the first turn would cover the players who skip.
The Hint button is a good safety net and I would surface it harder in the first match.
Small mismatch worth fixing since it sets expectations: your post here says "a match takes only a few minutes", but the setup screen says Small is 15x15, 6-10 min, Medium 10-15, Large 17-20. The game's own numbers disagree with the pitch. If 6 minutes is the real floor, saying so is better.
Last thing, on getting people to the board: there are six option groups before a first match (mode, board, opponent, first move, timer, end condition). For someone who has played twice that is great. For someone who clicked from a forum post it is a wall. A "Quick match" button using your defaults, with the full setup behind "Custom", would get first-timers playing sooner.
The paper-and-pen presentation is genuinely lovely — the torn notebook, the pens, the stick figures. That part sells itself.
I am doing the same thing with mine if you want to trade: a store and delivery-routing management sim, browser demo, no download — https://rldgamesstudio.itch.io/shelves-and-streets