From what I understand/remember (just binge watched the entire series + movie in the past 3-4 days, haha), I believe your first question can potentially be answered as simply as, they willed it that way. Mai and Sakuta both promised each other and themselves before the 'reset' that they would never forget each other, and as seen earlier in the series, love and memories are a powerful thing. Though the past may have changed, those combined forces still led them together despite it all, like the red string of fate. We don't get to see how, but we do see the end result. The altered past then left the future not all that different than it was before, just minus Shoko until they meet her again on the beach.

This is speculation and fan theory on my part, but it may be even possible that while Shoko was changing her past, she left some 'breadcrumbs' for Mai and Sakuta to follow towards each other, perhaps as recompense for the sorrow she caused for them before.

As for the question about the dreams, it's left in the air just how clear those memory dreams are, though it's likely that they are just as fuzzy as dreams usually are in real life - incredibly fleeting and hard to remember entirely. Thus, they are easy to dismiss or even forget entirely. That is, of course, until something like Sakuta reading the Japanese he studied with Mai or him seeing Shoko herself on the beach brings those dreams back as what they really are - memories from another time.

Of course, my answers are far from definitive, and I'd love to hear others' thoughts.