They say to change motor oil every 3000 miles or 6 months so I would say if the oil if a year or more older why risk your engine over a couple of bucks.
Depends on who "they" is, and almost certainly that's considering there are combustion byproducts in the oil.
I question the part about being opened. Is the insinuation the oil is bottled in a vacuum or some sort of special inert atmosphere bottling environment? I'm guessing not...
I asked Amsoil this regarding 2-cycle oil a long time ago and as I recall they said (paraphrased) as long as it's not coagulated or separated you're good to go.