All your questions are depending on your actual system. Back to the drawing board!

At the cold end of the MCHE in LNG plants where N2 content is less than max permissible, LNG is usually a little subcooled and so there is no flash gas (as with LNG produced in north Borneo). In plants where N2 content is higher than permitted ( Western Australia, some plants in the ME), the cold end exit temp is deliberately kept higher to allow a simple end flash to remove the excess N2, which will of course contain some C1 also. This flash gas is usually routed to the HP fuel gas pool. In plants where N2 content is even higher, a nitrogen rejection unit is installed ( frac column with ovhd condensor and a reboiler) to minimise C1 losses to the N2 reject stream.

Flash gas produced at LNG MCHE cold end is not the same as boiloff gas, which is vaporisation loss at the LNG storage tank.