Not at all, although there is a sizeable population that add that part to romantic roleplay.
A lot more don't get involved in romance roleplay at all, or if they do, just "fade to black" and mutually assume the characters had sex for storyline purposes.
A power poser seems to be their term for what others call a godmoder -- namely, each player has the right to determine what happens to their character. It's freeform roleplay canon since the genre started on IRC way back when...if your character is making an attack on another...don't say that it hits.
Examples:
XXX hits YYY over the head with a chair! <-- Godmoding/power posing
XXX swings the chair at YYY, aiming for YYY's head! <-- acceptable action
So when they ask that on that site to not be a power poser, they're asking to make sure that you have the permission of the player of a character you want to use in a story to use them and have them do actions. Think of it as "licencing".
LFG, you read the second part right. It happens, people write about it, Flowers of Happiness made fun of a few such stories/board threads back in the EQ1 days like
Palou the Lounge Lizard (NSFW, most likely).
There are a lot of people that play EQ2 for the roleplay factor, especially on the two roleplay servers. I'd venture to say a majority of them don't cyber, and of some that do, do it for the simple fact that it clearly advances a storyline and not for erotic purposes. But there are roleplayers out there that do cyber for erotic purposes.
Freeform RP (the style most use in EQ2 and other MMOs) started on IRC and AOL chat rooms. Some of the channels, like The Silver Blade Tavern on Dalnet and The Black Dragon Inn on wherever the hell they are now (started on EFnet) are still going, and have some pretty creative people playing out interactive stories that read better than your average fantasy-themed novel.
Some, like myself (I admit it, I roleplay -and- raid, *gasp!*) moved to EQ and later EQ2 because hey, we have a game to play and pretty graphics as well as people that have some interest in the fantasy genre and might want to roleplay.
Anyways, that was a ramble, but to answer the questions...
Power posers are roleplayers that even other roleplayers think are dumb.
Yes, some roleplayers cyber.
The majority of roleplaying is not cyber, even when involving roleplayers that do cyber.