It looks like there have been plenty of questions regarding guests bringing dates recently, but I don't see these particular situations- sorry if they are a repeat

Background on our wedding: getting married June 29th, invitations have gone out, venue has max capacity of 125, we invited 123. We wanted to keep the wedding small-ish, both because of cost and the fact that we aren't super pumped about being the center of attention, especially in front of lots of strangers.
One of my bridesmaids has never dated anyone, nor has she expressed any interest in dating anyone before. She is going to have lots of friends at our wedding, so we didn't give her a +1 on the invitation. However, yesterday we were at a party together and she says, "I can bring a date to the wedding, right? Because I already asked someone." I was a bit shocked and asked who, and she replied with "Someone I've been seeing a few times. I'm not ready to talk about it yet." I managed to sputter out that I would need to check the guest list...should I just let this slide to avoid drama, even though I'm pretty annoyed at the assumption?
My second question is about a date for my dad. My mom passed away two years ago in July, so obviously that wound will still be fresh and I know I'm going to be pretty emotional about it on our wedding day. My dad has tentatively been stepping back into the dating world recently, and this past week he springs on me that he has a new girlfriend. I've never met this woman and it's very new for him. I've got a lot of mixed feelings about it. Do I have to invite her to the wedding at this point?