Simplified:

On the HSK 1 vocabulary list, at CEFR level A1.

mén ㄇㄣˊ

    • gate door doorway gateway opening (CL:扇[shan4])
    • valve switch other door-like or gate-like structure
    • way to do sth knack method approach
    • family household lineage
    • sect school faction (religious or academic)

      bound form

    • class category division phylum

      bound form

    • classifier for courses, fields of study, branches of technology, relatives by marriage, guns etc
    • -gate (scandal)

      suffix

Where 門 is used

Sources