A second dog could help or you could end up with two that bark! And you do NOT want a second young dog that will go thru all these same behaviours!
Generally though most animals ARE a lot happier with a pal of their own kind to play with and interact with -- dogs tend to be a lot happeir with another dog, cats with a cat, though a cat and a dog even can have a very rewarding friendship.
In general though: you have a YOUNG energetic dog, still a puppy, who is doing normal young dog things. You need to both set some ground rules through obedience and consider putting some challenges to his brain (obedience training will be the start for that). You will almost NEVER be able to tire a dog out thru exercise -- mine routinely can walk 4-5 miles, and swim, and that will just be enough to give them a long nap, but they will be ready to go again an hour later. Obedience classes or agility, where they have to THINK, REALLY wear them out by contrast.
So the goal is to make sure the dog uses its body and its brain, not just one or the other. He doesn't sound overly bored to me -- you are doing lots with him -- he sounds like no one is telling him how he is supposed to behave and he is therefore feeling free to rudely DEMAND that you entertain him constantly. Of course he wants constant attention! That's what puppies and small kids want from adults! You have no obligation to give it though -- he needs to learn to politiely keep himself busy and relax as well.
Obedience work will really help wear out a dog and is also fun for the dog. I'd get Sam into a basic obedience class and when that is completed, get him into a clicker class or buy some books on clicker training and do some work with that -- dogs love it and it really makes them *think*. I do freeform clicker work with Jaspar for 15-20 minutes and he is exhausted after -- he has to keep thinking, thinking, the whole time! Google Karen Pryor and you'll get her clicker website for more info. If Sam hasn;t done obedience you really must get him into a class around now -- it gets more difficult to work with a dog that is approaching adulthood so laying down some basic work at his age is going to make all training much easier.
Obedience comes to mind more generally because you are not just talking about a somewhat bored dog -- you are also talking about a dog already showing impolite and unacceptable behaviours. He needs to know how to go into a downstay; he needs to know he goes on the floor when he starts pawing at you, he needs to know scratching doors isn't acceptable. To teach those more advanced ideas, you need a basic level of obedience that you can build on. Consifer what he is doing and compare what you would do if this were a toddler -- the toddler would be told firmly that the behaviour isn't allowed. Sam needs to be learning in the same way (and teaching 'quiet' would probably be a good idea too! :lol
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Regarding the treat ball -- why not buy an inexpensive area rug that you can roll up, that he can play around on?
Also: why was he alone and able to strip wallpaper in the hall? Uh oh!! Think of a young child -- out of sight, out creating mischief. :lol: He's still IMHO far too young to be out of sight -- by doing this he has shown he definitely isn;t yet old enough to be left without supervision. Puppies often strip wallpaper (Jaspar did in my hall); as far as he's concerned it is just another toy to explore and play with; it isn;t so much that he is bored per se but that he was able to get into something he shouldn't be able to get into.... which means from now on, keeping him under watch and *closing doors* or babygating off areas where you know he could be destructive.
