The first time I started Act 3 I was at the bulletin board and was offered a house for 5K. I made an error playing further down the game and restarted again. This time no one offered me a house. Is this normal? Will another offer come along further into the game?

No, the option should be there => the man in the house of the Keeper of Ranks, did you ask him? There are 2 in this house. But I'd wait a bit, until you met and helped Fred - then the house costs only 2500.
Kiya