Hmmm...
Why do Pokemon not die in the games? Are Pokemon trained never to use more force than necessary to knock out? Does that apply to a level 100 legendary using Hyper Beam on a level 2 Bidoof?
While I want to shout game mechanics, I generally believe that within Pokémon battles, restraint is used as to make sure that no Pokémon is seriously injured. Various Pokémon that might not be able to defeat a foe in honest combat could easily use a move such as Psychic to strangle their opponent or in the case of fire types, increase their body heat in order to incinerate the competition.
Do Pokemon get diseases like normal humans, and can they die of old age? Or are their only cause of death at the hands of other Pokemon or people?
One most keep in mind that not all Pokemon are alike. Pokémon such as Venomoth are stated to have extremely short lifespans among the Pokemon world while Legendary and artificial Pokémon such as Golurk and Groudon have existed for thousands of years, with Arceus existing for possibly billions. So in that vein, it seems that while certain Pokémon might have the same mortal qualities as humans do, others are extremely likely to outlive their trainers, if not humanity itself.
Considering the fact that exploring entire regions has never brought up a structure as large as Pokemon Tower but connected to humans, does this send the message that Pokemon death is more important than human death in this world? Is this the right message to send to children, or do you think they wouldn't pick up on this anyway?
That is also based upon the context of what Pokémon you're talking about. An elderly Pidgeotto passing might cause grief among it's trainers, but that's nothing compared to what would happen if a Major Pokémon such as Dialga or Palkia were to fall, which would cause disruptions to the very existence of the fabric of the universe. I don't see what the Pokémon Towers have to do with humans being less important then Pokémon, they just seem to be there to say that most Pokémon aren't immortal.
Do Pokemon feel death the way humans do? Do they understand that it's a part of life, especially if they were raised in a Trainer's care so they didn't experience death often?
Most Pokémon seem to have some type of understanging of death. Animialistic creatures like Rhydon and Ursring view it as part of the natural cycle, humanoids like Alakazam and Hitmonchan view death as something imminent to them in the same way it is to humans, Yamasks already died once, and so on.
One thing that is devastating to many Pokémon though, seems to be the scenario of having to watch their trainer die. In the case of Sigilyph, losing their trainers caused them to go into some form of denial, making them follow flight paths they were ordered to roam in order to defend their long gone civilization, seemingly ignoring the fact that there is no longer anything to guard. Others, such as Dragonite, grow bitter and distrusting of the outside world, forever shattered by the fact that the person who raised them is no longer there, shunning the outside world, eventually breaking down to becoming wild again.
Do Pokemon go to a better place, or do they believe that they do?
As implied by various Ghost types, Pokémon do indeed have a soul of some sort, and though the Anime canon may not be the same as the game canon, it is shown that there is at least some form of afterlife for Pokémon shared with by humans.