1 - May only attempt to catch first pokemon encountered per area.
2 - If it faints, it is treated as dead

3a - Only normal type damaging moves are allowed.
3b - Each pokemon may have a maximum of two stat altering/pure status inducing moves of any type. Stat altering/pure status moves can be of any type.
3c - For the purposes of these rules, hidden power/fling/nature power etc will be treated as normal type moves.

For gym leader, rival, rocket execs, elite four, champion and legendary battles, the following also applies:

4a - Move selection is determined by drawing playing cards [Each suit assigned to one of the 4 move slots]
4b - To use an item, a coin must be flipped and land heads.
4c - If a pokemon faints or an attempt to switch out is being made, a die is rolled to determine the next pokemon sent out.
4d - Upon drawing the joker, any move [that does not break the third rule] can be used that turn. [In other words, the joker can be treated as whichever suit the player wants it to be.]

4e - Each time a battle of this nature is won, one attempt may be made to capture a pokemon via the pokewalker

by Xetaja