look on the back, it will have a sticker that stated the product number, and the month and year it was built.
you can register it, and as long as you have the receipt from an authorized dealer it will be under warranty.. if not then usually youre out of luck, no matter who the manufacturer is.. in my case, i bought it from an unauthorized dealer so the warranty was void, however since i emailed the customer service they were very kind and said they would allow the warranty anyway.
as for the remote, its not the best in the world, but it does program to the sony dvd players. i have one, and it works fine. buttons are a little confusing, and youll have to mess around with it to figure it out. the manual is also a little confusing but all the information is there. you dont seem to have any real problems with this reciever yet. if you need a better remote then you can buy a logitech harmony. those are supposedly the best ones out right now.
the 335 remote programs to my sony tv, sony dvd player, and sony ps2 just fine.
although some of the buttons arent there, most of them are, and onc eyou get used to it, it will work fine.