Yes or no?

Are you kidding?

Best not to

Continue to have chats with her for now but best to keep it professional.

If you ever "ran into her" in a shop or wherever, you could suggest going for coffee.

It doesn't sound weird Sikipoo - sometimes we meet people in random but regular situations with whom we just 'click' and think how nice it might be to have longer chats with them.

However, I think you should rely on your instinct - you feel awkward for a reason.

Just enjoy the banter when you go to your appointments.

why not?

I suppose you could ask her?

In this sort of situation, I think, what are the cons of doing it?
What have I got to lose?

And go from there.

Your post is a straight forward yes or no.

No.

I actually made friends with the receptionist at a PT office where I went twice a week for a couple months. When I was finished with PT, I said, hey maybe we could grab lunch sometime. She happily encouraged me to text her. We've had lunch a couple times. Other times, we've just texted. I'm a really outgoing person though. So maybe that's why I felt fine extending the invite. Plus, she's older and single so I figured she'd be happy for a new friend. Hope this helps

No. Because if she refuses you might feel awkward dealing with her in future.
Enjoy the chats you have when you see her.

No because she’s his wife and his profession is regulated. Keep the boundaries absolutely clear

Just take her as part of your day and move on. I meet some lovely people on the bus, in the shops, at the dentist. They are just that, part of my day. Anything else sounds weird!

Only if you change your osteopath first.