Hints: Paying the landlord:

Give the betting slip to the barber. He'll ask you if you want to
make a bet. The odds are 25:1. You will now have enough money to pay
the landlord.

Hints: Proposing to Frankie:

Give the ring to Frankie after rescuing her. She will respond that
she has to think about it. Stop in to see her before going to the
police with the diamonds and show them to her. You'll receive a kiss
and she will accept your proposal afterwards