Rules or constraints for assembling the cards in your Pokemon deck
Basic stuff like your questions are handled by rulebook.


  (...) assemble your own deck (stack of Pokemon cards) prior to coming to the game/match/fight/battle. So by the time you get to the battle, you already know what cards are in your deck, and you've intentionally selected for them to be there.


Yes, that's right. (rulebook page 22)

From time to time, there are also special tournaments where you build a deck from cards you get from organizers just before the tournament starts (and no other cards) so you don't need a preconstructed deck.


  Is there a max deck size (max # cards) a player can bring to a battle?


Unless stated otherwise, Pokémon TCG deck has always 60 cards. (rulebook page 22)


  Is there a max # or % of Pokemon/Trainer/Energy cards you can have in your deck?


At least one Basic Pokémon is required. Cards are limited by their name - you can't have more than 4 cards with the same name in your deck (except Basic Energies). No other limit exists. (rulebook page 22)

On all official tournaments, there are additional restrictions on cards that can be used.


  Do you have to shuffle your deck prior to play?


Definitely yes, Pokémon TCG is based on randomness, random drawing is one of the core concepts. (rulebook page 8)


  What happens when you run out of cards in your deck during play?


During your turn, nothing. But drawing at the beginning of your turn is mandatory, so if you can't do that, your opponent wins. (rulebook page 8 or 10)