I'm currently playing games against Aya, and after the game ends it does a sort of 'post-game analysis' where it shows territory, dead stones, unclaimed territory, etc.

What are stones that have dots on them? Does it mean they are neither dead not claiming territory? In the example board I've attached, all stones with the circles I'm referring to have circles belonging to the opposing color, but they aren't the clear "X"s either.

I suspect the circles as opposed to X's means something like "probably dead" or "dead but may have some aji". E.g., after B plays 5-14, W needs to play 2-18, or else there will be trouble. (The dotted white stones are just dead, but maybe aya is still pining after them.)

There are no stupid questions!

You mean after B played 6-14, W must answer in the corner, otherwise another B move on 5-18 would kill (interesting position BTW). W should rather answer on 4-17, since 2-18 looks like self-atari

Maybe W answering at 5-18 is slightly better, because after that, any B move in that corner will be self-atari for B.

Yeah, clearly the upside-down number-number grid had me reeling... I meant 6-14 and 5-18. I don't think 4-17 vs 5-18 actually makes a difference, as it's one ko threat in either case, but I agree with Ed that 5-18 is more satisfying.

After posting this it occurred to me that the dots might be dead and the X's might be "you need to add a move eventually". That would credit Aya with understanding the Lower Right. But Canarmane seemed fairly confident that X was dead.

This is slightly off-topic but the 19-19 point in the upper right is not exactly a neutral point. When it is occupied by a stone Black and White will have to defend the cuts. It won't change the score, though.

I'd say it's neutral because neither can play it without first defending the cut. After one player does so, so does the other, and the point still is neutral.

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Patience, grasshopper.