Unless I am very mistaken, the Postal Service takes very seriously the delivery of ALL of the mail ... it may well be illegal to hold back any of it unless you have filed a written order (I think they have a form for this). You can easily recycle unwanted mail yourself.
The newspaper delivery issue should be taken up with the newspaper office.
I think the paper carrier should be tipped (and maybe not just at the holiday season) - it's a hard and underpaid job. You should get good service regardless of your tip, but I'd give the kid a break.
Its been a long time since I changed addresses but I think "Jane Smith or current resident " could be forwardable. So the mail carrier had the option of forwarding ti to the new address for Jane Smith, i'm not sure ?
Having moved a lot, if something is addressed as "Jane Smith or current resident," it is usually not forwarded. But I think that has to do more with the class of mail that it is sent under, rather than the address. First class and priority mail is forwarded. Standard mail is not--that includes circulars, books, catalogs, and advertising mail--which are the types of mail that would get "or current resident." Magazines are forwarded, and I think the Post Office may even send the magazine your new address.