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@rhb
From the picture posted, I think this is the relevant techdoc from Shimano for correct installation and setup of the rear mech on your hybrid.
Print ( or enlarge on screen) and follow step by step.
http://techdocs.shimano.com/media/techdocs/content/cycle/SI/Alivio-Acera/RearDriveSystem/SI-R920A-En_v1_m56577569830612828.pdf
Before doing all that though, grab a bare bit of rear mech cable (under the downtube is a good place) and give it a good pull outwards from the tubing. If this pulls the mech over without any trouble it's probably not seized. If it feels tough / binding - replace inner and outer(s).
P.s. Position of arm changes relative to gear selected, so difficult to answer your last point on that.