On the help part, it exactly says as you're guessing: Helping somebody win will net you no rewards, and the battle deck is a different deck from your profile 5-card list. The note there is warning you that the card selected for help will be the main one in your deck, not in your profile.

The trap advice is the following:

Decks in PeroColliseum are usually decks of Moe 5 and Moe 4/Sexy 1, given the percentile winning probability.
I will say that the most victorious defence deck is a daring Moe 3/Sexy 2 and the trap deck.
But this happens to be a very unsuitable deck for attack, becoming very troublesome because it's necessary to change decks every time between attack and defense times.
That's why most of the trap decks just wait until they are attacked, and then arbitrarily decide to counterattack.
Try to set your attack decks with the understanding that there will be such decks in play.