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The easiest way to modulate from G to F major is by modulating down to C major on the way. In that way you are moving down the circle of fourths/fifths.
The corresponding minor key to G Major is e minor. The key signature will be the same, one sharp: F#.
The dominant 7th chord is composed of the root, major third, perfect fifth, and minor seventh. The dominant seventh for the F# key would be F#, A#, C# and E.
It depends on which key you are referring to, all the keys with flats are: F major (1 flat) B-flat major (2 flats) E-flat major (3 flats) A-flat major (4 flats) D-flat major (5 flats) G-flat major (6 flats) C-flat major (7 flats) Likewise the relative minors are: D minor (1 flat) G minor (2 flats) C minor (3 flats) F minor (4 flats) B-flat minor (5 flats) E-flat minor (6 flats) A-flat minor (7 flats)
The relative major key of Gb minor is Bbb (double-flat). However to make life easier, one could just say the minor key is F# minor and then the relative major would be A.