When indoors, FLF's need lots of direct sunlight and constantly damp soil. Not getting enough of either can cause the brown patches on leaves. It is a tropical, non-seasonal plant that has no dormant period. It may grow a bit slower during the shorter days, but it never goes dormant and should never be allowed to get very dry.
Misting does not help or harm. Trimming off discolored leaves or brown patches will not affect the health of the plant at all. It will just make it look better. Existing brown leaves will never recover.
If you have a sunnier window, move it there. The more light t receives, the more leaves it can support. Allow no more than the top half-inch of soil to dry in between waterings. It will take some time, but you will see fewer brown patches and more healthy new leaf growth.
