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.

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.