The analyses of a text #1

The protagonist, Philip moved in with his uncle Mr. Carey, the Vicar of Blackstable after his mother's death.
He goes to the medical school St. Luke's in London.
He came across his ex-girlfriend Mildred on the West End, found her being a prostitute, and she moved in with him.
Now Mildred talks to him about the land lady.
........................................
"She's a very nice woman," said Mildred. "Quite the lady. I told her we was married."
"D'you think that was necessary?"
"Well, I had to tell her something. It looks so funny me being here and not married to you. I didn't know what she'd think of me."
"I don't suppose she believed you for a moment."
"That she did, I lay. I told her we'd been married two years?I had to say that, you know, because of baby?only your people wouldn't hear of it, because you was only a student"?she pronounced it stoodent?"and so we had to keep it a secret, but they'd given way now and we were all going down to stay with them in the summer."
[Of Human Bondage by Somerset Maugham]
1. I'd like to know if "I lay" means "I bet."
2. I'd like to know what "they'd given way" means here.
3. And I'd like to know if you think "them" refers to "your people."
Thank you in advance for your help.