Hamtaro was one of the Helpful Hamsters (another Ham-Ham gang created by Ritsuko Kawai and have their own comic in The Official Hamtaro Handbook) before he was bought for Laura.That could be where he learned to be a problem solver. And all their names begin with "Ham" just like his.
The Ham-Hams are just dying to tell their owners about their awesome adventures.But alas, they must fight the temptation because that would mean letting their owners know that they can talk and that they leave their houses into a dangerous world on a daily basis.
The Hamtaro video games take place in a near future post apocalypseThe games at the very least take place in an alternate universe where the Ham-Hams don't have owners (they are never mentioned) and live at the clubhouse and humans are never seen but must exist or have existed because of the human sized buildings and object littered throughout the worlds but humans are never seen. If this is the case then humans might have disappeared less than a year before the games' events.
Boss is a Time LordThe Ham-Ham Clubhouse is his TARDIS.
Howdy is gayAs if him saying he'd receive a valentine from Oxnard in "Valentine's Day!" wasn't a big hint. Any evidence of him liking Pashimna is just him trolling the other Ham-Hams into thinking he isn't gay.