Is it friction shifting? If so as long as the limiters screws are adjusted correctly, couldnt most of those problems like the chain hanging and the noise be potentially because the rear derailer isnt lined up directly on a cog? If youve been riding 6speed for a long time it may take a bit of time to get used to the smaller distance between cogs on a 7speed.
My old schwinn had 6 and my new ride has a much more modern 7 speed cassette, ive been constantly overshifting bothvup and down and having to finetune mid ride to get rid of noise
Forgive me if ive misunderstood, I just always try and eliminate any adjustment errors before assuming that a part is bust or that theres an inherant inability to "get along" with another component.