Re the wobble, surely the action just needed bedding in to the stock a little ? I've had to bed 2 rifles & a Boyds laminate stock, all brand new.
Re the "new" rifle, I've only ever bought 6 rifles new, only 2 of those were "out on the rack" & in both cases I asked if they had one still boxed rather than the display model & bought the boxed one,
in truth 1 of those probably doesn't count because the one in the rack was wood & I wanted synthetic.
Bit naughty passing off a pre-owned rifle as new, even if you only had it for four days, but should come to light when the new owner tries to register it.