The PPC is itself a continuum. Some agents are aware that they have writers. For example:
July's agent of the same name discovers the Internet and (briefly) her Author:
Recursive Behavior
Also, part of the job of the DIO is to assassinate Mary Sues that have infiltrated the PPC. Sure, some of those are just Sued PPC agents who've been exposed to a little too much glitter and been "assimilated"; but some of them are PPC agents written by PPC badfic writers. Jaycacia Thornbyrd is one famous example; you might also check the DIO web page; there are a couple of missions there. (Both things are linked on the wiki.) Note that the DIO neuralyzes regular PPC agents who come in contact with its agents; the PPC in general doesn't know of their existence.
So, basically, the PPC is a continuum like any other, a Word World connected by plot holes to all the other continua (except quarantined continua, ones where the author has forbidden fanfic). I've seen multiple instances of agents able to see their own Words, such as when an agent gets annoyed and speaks in allcaps and someone else tells them to stop speaking in allcaps. No-Drool vidoes got the nickname of "ellipsis debriefings" in one fic, in which an agent was summoned for "a ...debriefing." Similar things happen all the time.
So it's safe to say that particularly observant PPC agents do know they are fictional characters, and a few have even speculated about their Authors; but in the world of the PPC, fictional characters are real (that is, sentient, if they're written well enough). World One is special because it has such a high plot hole density. We don't know what, but plot holes tend to be instrumental in the creation of worlds (the Cascade, which created HQ, was a plot-hole-driven event). World One residents, if they have the ability, can become Authors, and mentally connect to different continua, either an established one or an undiscovered one. Whether they create new continua or just discover them is unknown (I tend to think they discover continua that exist already, in a multiverse where literally everything that could ever happen, does happen.)
To think about how visiting fics works, you have to think in more than three dimensions. Every canon is a continuum worlds, with not just the actual canon that does happen, but AUs that could have happened. A Mary Sue creates natural, uncontrolled plot holes, dragging canon out of shape and into dangerously improbable configurations; PPC agents create controlled plot holes that let them insert themselves into the fic in order to repair it. The main canon is the most probable arrangement; good AUs are the most probable of the alternate possibilities. A story is made of what does happen, and also of what could have happened. When uncontrolled plot holes damage a continuum, they connect extremely improbable possibilities to the main canon; and information can leak through them to damage the main canon. Eventually, left unchecked, the information becomes nonsense and meaningless, and loses its organization. In the end-stage, no usable information is left at all. Wild plot holes endanger the continuum because they damage the organization of the information that makes up the Word World.
If you need a 3d representation, think of a continuum as an infinite number of time-strings, stretching out into the distance. Each string is a world and all its events (at least four dimensions, possibly more in sci-fi continua). In the middle is the Main Canon, connected by goodfic and good AUs to the strings nearby, which are alternate possibilities, pulling (by way of information transfer, not physical force) on the Main Canon. These connections can't pull it far out of shape because they are so close to Canon; in fact, they strengthen the canon the way a rope of ten strands is stronger than a rope of one strand. The problem comes when a Suethor connects an extremely far-flung world to Main Canon. A string very far away from the main canon will pull it out of shape much further than one that is close; and because they are so far away, cannot strengthen the main canon; in fact, it pulls the main canon away from the goodfic and good AUs that give it some of its strength. This connection is the Mary Sue, the Author-wraith, or some rarer manifestation of natural plot-hole formation. Sever it, and the main canon springs back into the middle, where it should be. Let it be, and the nonsense from the least probable reaches of the continuum begins to destroy the order of the world.
When PPC agents visit a fic, they aren't, technically, visiting Main Canon. They're visiting a stretched version in which the Mary Sue exists. Even when they remove the Sue and canon returns to near-normal, they aren't, technically, visiting Main Canon, because Main Canon doesn't have PPC agents in it. Only when they leave to return to HQ does the Canon completely return to normal--though, because PPC agents represent goodfic, their presence wouldn't damage Main Canon any more than normal goodfic does even if they chose to stay.
Because every badfic stretches the Main Continuum in a slightly different direction, PPC agents don't tend to meet each other, as they are in different subcontinua. The one exception is a Ficverse Fusion event (has a wiki article; has only been observed once or possibly twice if the Les Miserables Songfic Crisis event was an example), in which very similar words cause two alternate sub-continua to merge.
Yes. PPC agents--especially those who drop through plot holes from World One--can write, read, and review fanfiction. There are actually some PPC agents who used to write badfic and have had to kill their own work.
Most PPC agents join the PPC after falling through a plot hole to the PPC; but quite a few are brought through plot holes by agents in the field. The PPC itself is a continuum made of an infinite number of sub-continua.
Brain hurting yet? Good. :)