1. Yes but if feet are deteriorated just in one end it may get a waggling movement. So yes that is to make sure no tilting axial resonance is the problem. yes it is a abnormal nice looking vessel. However not all oil problems are showing external in this case from last year it was parts of a broken gear that showed up in the oil. It that case nobody did look at the oil, they just swapped filters and oil so it happens.
So next is if you did look at the coupling but normally it also should get some indications in the generator but there are exceptions. Some generators have a axial bearing in the free end so the generator shaft expands in to the gearbox or diesel when getting warm and OEM claim it is supposed to be like that and it require larger axial play in the coupling to take care of that or you get axial problems in the gearbox/diesel.
So yes in the end it may be a cylinder unbalance maybe, just to check the obvious I take a vibration reading at all injectors to sort out if there are any that is different then it is worth to check them.