“Shows up out of nowhere”
Out of nowhere means suddenly, from no obvious place, and show up means to appear, so the phrase means "appears out of nowhere." The subject She at the start is left out, which sounds conversational. The character who calls the heroine special and gives her courage mirrors Tina, who called Frank special in A1-01. Frank is the one who mirrors the heroine.
“It reminded me of us.”
Remind A of B means to make A think of B. Here A is me and B is us: It reminded me of us. means the novel made Tina think of the two of them. The next line, Of the night we met., says what it reminded her of.
“Anyway, back to the book.”
Anyway closes a digression, and back to … returns to the previous topic. Tina tries to move from memories back to the book-club discussion, but Frank continues talking about the details of the clock.
“that clock was two minutes slow”
When a clock is slow, it is not moving slowly; it shows a time earlier than the correct time. The clock showed 11:42 p.m. and was two minutes slow, so it was actually 11:44 p.m. The punchline is that Tina wants to get back to the book, but Frank insists on stating the exact minute they met. This builds on the late-night lab and the ticking clock in A1-01; the specific time is added in this episode.