In the first case, I would tell her…
“I am so happy that you’re feeling better and want to resume inviting guests, AND I would truly love to come, as I have in the past, BUT, I really feel you’re going a bit too fast. I would feel too guilty to be causing you to do the preparations for my visit, when I think you should slow down and take some more time to recuperate. In a month from now I hope you’ll ask me again.”
In the second case I would definitely take the number so as not to insult the person, and if you don’t want to call, don’t.
If they ask at a later date, why you didn’t call, you can always claim to have been very busy or whatever.