(1) Would you buy a refurbished AV Receivet from an authorized factory dealer like A4L?
You have received lots of good info. Please let me summarize.
Refurbs can either be done by the manufacturer, or a third party. When the mfg does it, they use the same tests and quality processes used on their new-build line. When a third party does it... who knows.
A factory authorized reseller, (like A4L), gets their refurbs from the mfg. So you know they got the mfg's standard testing and quality. AND they carry a warranty. The warranty is usually not as good as a new product, but generally good enough to assure there are no mfg or workmanship defects. And the reputation of the seller is important IF you ever have to use the warranty. Some sellers are easy to work with, (like A4L), and some are difficult.
A product falls into "refurb" status any time the mfg gets back a product that has been opened. That's why new boxes have tamper resistant seals... so the company can tell if it has been opened. Once opened, it cannot legally be resold as "new". And once opened, the mfg can never be sure how or how much the system was used. It may have just sat on a dealer's shelf. It may have been opened by a customer who never plugged it in. It may have been abused. It may have been used normally, failed and returned.
Out of all the possible reasons for a refurb, the only risky one is the unit that was returned and replaced for an intermittent problem. Like your car or any other product, it's hard to fix a problem that doesn't fail for the technician. So it is possible a system had an intermittent problem, the customer wanted it replaced, the mfg went through all tests and quality checks but couldn't find anything, and the system is sold as a refurb. It happens, but not often. This is where the warranty will help.
All in all, if you buy refurb from a reputable dealer, (like A4L), you can save some money with little additional risk.