(a) Why did she do it?

They had sex.

Edwin had just heard his ex-wife had died - he would have been (though he wasn't showing it) in a pretty fragile state, and in the state of mind where it is, frankly, quite easy to end up having sex with someone you would normally never have had sex with. More people fall into bed with the wrong person right after a funeral than at any other time. (Okay, this is based on anecdote rather than data. I'm not sure anyone's done a survey.)

I agree with jonquil that Karen was, very likely, also in a fragile state - a quietly-despairing they-say-women-can't-be-scholars-oh-god-suppose-they're-right state. It wouldn't be - it isn't - at all unusual for very bright young women to be completely messed up by the attitude they get at Oxford from the male students and the faculty.

I bet she and Edwin fell into bed together and that Karen - who is, after all, a thoroughly strait-laced, well-brought-up girl - felt this meant she ought to marry him. And that Edwin, who was probably contemplating with horror the thought of either leaving his children with their grandparents or looking after them himself by himself - threw whatever sense he had to the wind and proposed.

Agree with you about points (b) and (c).