You know, reading your description, I am really surprised that she isn't an oversharer as well as a nosy parker. She has such a high opinion of herself, her ambition and paranoia that personal info = career death must be the only thing stopping her. Based on how you describe her personality, I have devised the following theory...
I might suggest returning her questions onto her. No one should ask something they aren't prepared to answer themselves. It is also considered polite, no you could even say it is expected to return some probing personal questions if you are trying to get to know a person
. The trick is to ask in a very friendly and excited manner, like you can't wait
to hear about her own marital status, or her children or whatever it is she is bugging you about. I realize you don't
want to actually talk to her, but since she has indicated she doesn't want to share personal info you would actually be doing a little reverse psychology on her. Like when the rabbit begs the fox not to throw him in the deep dark
You could drive her away with your redirects.
She asks about your love life? - "Oh you know me perpetually single - but enough about me what about you any good prospects lately? *big smile*"
She asks about kids - "Nope no kids yet - are you
planning on having any?" *big smile*
She asks about retirement - "Eh not yet. Are you
looking forward to it?"*big smile*
You see, you can come across as operating on the assumption that she is bringing these things up because she has a personal interest in them, and you are politely giving her the opportunity to talk about it. Because you are so sweet kind etc. etc.
And if she says no no she wants to hear about you - "Oh well there's not much to hear on that front when it comes to me
. *puzzled look* I thought you wanted to talk about it because you
were interested in getting married/having kids/retiring/etc. Huh. Oh well! Guess if neither of us cares then we can get back to work!"
Basically, with enough false cheer and feigned polite interest, you might be able to reflect her nosiness back on her and send her scurrying before she has to give up any valuable personal info.
That's my idea anyway.
As to the dinner invites, PPs have given you good advice and basically told you what you probably already know: spit-polish that darn spine and politely decline!