Ha, getting distracted by chatting is half the fun of it! And no, you can't lock yourself out of the case. The evidence (the brass shavings, the repair tag, the old photo, the empty key hook) all turns up in the main story, so you'll find every key clue whatever you do with your afternoons.
The free afternoons decide who you grow close to: Mira, Theo or Juno, and who walks the lanterns with you at the end. Whether you solve it comes down to how you read the evidence on the board and what you name as the reason at the end. Thanks for the question, enjoy Hollin!