A pinch hitter takes the place of the person he replaced for the duration of the game – both in the lineup and in the field. He can, of course, be replaced by another player just as he himself replaced the first player.
Pinch hitters happen in the American League all the time, and have absolutely nothing to do with the designated hitter rule. (which is the only difference between the AL and NL)
“less often”, yes. But still frequent. A manager will put in a pinch hitter towards the end of the game, putting in someone on the bench to replace someone in the lineup who isn’t doing well or has a poor record against the pitcher. It still happens all the time, and to say that someone doesn’t see a pinch hitter very often because they only watch the AL is nonsensical.