Is she being invasive/ inappropriate?

Her primary concern is probably her children's safety, but she's probably interested in your safety too. If you are in a new environment/place maybe she just wants to make sure that you're not being taken advantage of by someone, and that your new friend really is someone you want to be friends with (not just someone she wants you to be friends with).

If you don't want her to come, just say that your friend works/looks after her gran/plays tennis at that time so can't make it. Or you could accept that when you work for someone as personally as you do, they are going to take an interest in what you do outside of work, and invite your friend around - I'm sure everyone else will have a perfectly nice time and once it's over with, your boss and friend never have to meet each other again!

I completely understand your feelings, but I think this time you had better just be gracious and charming and enjoy the tea party. As long as your employer is happy with your friend, that will earn you some brownie points and she may not worry any more. Don't overlook the fact that she may be worried about your safety. You are, although officially an adult, still young, and living in her house, which gives her some responsibility, which she is taking seriously. Don't give her a hard time, or act like a rebellious teenager, or she'll get stricter with you!

If I had an 18 year old from a foreign country living in my home I would feel responsible for her and would want to make sure she is safe.

I agree that who you hang out with is none of your bosses business but being "nosy" is, I think, a sign of caring in this case.

Personally I am happy to introduce people I know to each other. I wonder what you have got to hide.

That does seem to be rather "over the top" -- however, I would go ahead with the friend/boss meeting.

In the next few days I would have a quiet word with your boss, letting her know that you would never interact with anyone unsuitable, because you have been raised properly, and that you'd hate to think that she would expect to appraise all of your friends.

No. Your time is YOUR time and you should not be accountable for who you choose to spend time with away from the job.