What Radio stations on LW and MW the rarest in night?
That’s difficult to answer since it depends on a lot of factors. I would say any MW or LW signal that’s not normally broadcast for your area is worth trying to hear. In some cases you may be able to hear stations VERY far away if conditions are right. One type of LW signal I’m actively trying to get as many as possible is aviation NDB stations (non-directional beacons). These are rapidly disappearing due to GPS and other navigation systems and will someday be gone from the airwaves.
A good source for MW and LW stations is MWList.org . You can get more info about LW beacons (including NDB’s) via https://rxx.classaxe.com/ . Both sites are very comprehensive and will require some patience to navigate.