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In strict classical harmony the seventh of any seventh chord (in any inversion) is the dissonant note and therefore the one that must be resolved (usually down by step). Some seventh chords contain tritones (which also must be resolved according to traditional harmony rules) and therefore multiple voices have to move, but in a minor or major seventh one can resolve the dissonances one note at a time (eg Fmaj7 [E is dissonant, resolves down] -> Dm6/5 [D is a correct resolution, but C is dissonant] -> Bø4/3 -> E7 [G# and E are correct resolutions, but D is dissonant] -> Am. One could theoretically resolve to Am earlier by cutting out the Bø4/3, but this would create consecutive fifths between the Dm6/5 and the E7, so the chords would have to be revoiced. One could also create a "cycle of fifths" progression by resolving two notes at a time - Fmaj7 -> Bø4/3 -> Em7 -> Am4/3 -> Dm7 -> G4/3 -> Cmaj7 etc) To answer your original question, the E of an Fmaj7 chord does have to resolve to D (or F, in which case it's not an Fmaj7 chord at all but a plain F chord with an appoggiatura), but Fmaj7 and G can't be placed side by side in the first place because of the consecutive fifths (you'd need to interpose some other chord, e.g. a D6/5). To answer your second question, that would be correct under the following circumstances: (1) the Am7 chord on the first beat is a "double appoggiatura" to the F6 chord on the second beat; (2) the Am chord on the second half of the 2nd beat is a passing chord between F6 and B7 (4/2) (G6/5 would also work); (3) the treble A moves down to a G. I would also move the 3rd up an octave as the chords will sound better and cleaner that way. This is an example: