You have to use an AR. Otherwise you can't. There may be cheats without need of AR but you can't.
no
only if you have the catch trainers Pokemon code
battle trainers or catch the Pokemon
you dont
You can't actually catch him in Pokemon platinum but you can migrate him over to platinum if you have him in another game
Action Replay
I don't think so but check victory road. Y do you need them anyway? you cant catch trainers Pokemon unless you have an action replay
You can only do that by buying an action replay and entering a code titled "Catch trainers pokemon" so yes it can be done but only by methods of cheating.
press l and r while playing the game
I don't think you can but if you have an Action Replay you could catch the trainers lapras.
If you mean another trainers Pokemon you have to use cheat codes
Never in any game of Pokemon can you catch every Pokemon on one version of the game you must use the other versions to get the rest. Unless you cheat but don't its not worth it.