I've bottled a 10 month old batch in a primary bucket still on the cake. As long as the airlock doesn't go dry and your vessel is sealed you should be ok.
Moving/swirling/shaking(gently) the liquid will help dissolve CO2 in to solution but isn't necessary to fully carb a batch and will stir up your sediment for the short term.
Bitterness slightly subsides, but aroma vanishes.
You will likely get drinkable beer, but if you are shooting to make a specific style/recipe...I would use fresh.
I've used cheesy smelling old hops I've had for about 2 years and the results were a very mild hop aroma (no cheese) but they...
Give us your definition of open system...
If temp is relatively constant and its got an air tight seal and a way for carbon dioxide to escape you will be fine for a very...very long time (if you manage keeping the airlock from drying up).
I have left beer in my primary bucket for 10...