Should have no problems, as long as it is plugged into some sort of surge protection.
I leave everything except my TV, class A amps & multi channel amp (it has a trigger) on all the time. They are all on line conditioners. If I leave town, everything gets unplugged except the Battery Power Supply for my Rowland amp. Most modern solid state equipment runs relatively cool, and many engineers/techs say it's better to keep it at a steady temp. I agree, I've never had a component fail from this practice....
Yes, but listen to tuner turned on/off. Digital tuners have a nasty habit of throwing EMI/RFI onto the power line. If you hear degraded performance of other sources, chances are If you want to leave on 24/7, you may decide to invest in a audio specific power line conditioner utilizing a "isolation" technology.