The baby thing is a ridiculous rumour with her last 3 pregnancies Kate has been bed bound/ hospitalised with Hyperemesis gravidarum. She missed George's first day at school she was so sick.
Yet we have seen her lots in the last few weeks so either she's into her second trimester when I think she was feeling better in previous pregnancies or she's not pregnant. She doesn't look like she's in her second trimester to me!
There will be speculation about a 4th child till they either have one of the papers decide she is to old to have one.
In the documentary from a while ago one of the journalists interviewed said the papers want a story they don't care what it is but royals sell papers. As William and Kate don't give the press stories I think we can expect a lot of speculation articles in the future unfortunately.