Seclusion

Q: I am a married male attending a course over the weekend as well as a married female who lives in my street and belongs to the same running club. The course location is about 10km away from our houses and she suggested we travel together on Saturday and Sunday to and from to save travelling cost. Is this advisable?

Q: Is it permissible for a baaligh male to receive maths tuition from a 60 year old ghair mahram woman?

Q: Can two women travel in a car with a man who is not mahram for both for a short distance?

Q: May a woman go to a male doctor for eye laser surgery (to correct her eye sight)? There are no female doctors available to do the operation.

Q:

1. When I was in an elevator/lift in Makkah together with a Saudi man, 2 women in full hijab and niqab entered the lift.The Saudi man got upset and chased them out. I used to often be alone in the lift with women and used to be unsure what to do. Is it  permissible to be alone with a woman in an elevator or what should I do in such case?
2. If my seat on the plane is next to a Ghair Mahram woman, is it ok to sit next to them?

Q: If a shop owner ends up being alone in his shop with a female customer, is this counted as impermissable khalwa? (although another customer might enter the shop at any time). Also, in my local library the librarian is a women and sometimes we end up being alone in the library (although others may enter at any time), what is the ruling in this case?