for this point
Liz Bathing scene – on Tuesday and Sunday afternoons after you build her a new house
where can i find the location of this house to build it?
did you use a fertility potion?
Go to the oracle and get a fertility potion recipe and brew it in the shed (or just press the yellow button outside MC's house to get 10 potions, Be warned this is a cheat button and it will give you gold level ups and weapons), drink it before having sex it will increase your chances greatly
You have to advance in the "Not so royal affair" quest and tell Walter a lie before advancing with the pregnancy.