Hi AJ,
I'm not that experienced in the music business and so can't give you much explicit direction, but I can lay out some basics in wide brush strokes which may help you in your research while you wait for someone more knowledgeable about the music business to jump in.
Basic principle one: if you create an original work of authorship (music, poetry, art) in a fixed medium, then you have a copyright in it.
Two: If someone else uses your work to make a new work, that's a "derivative work". They need your permission to make the derivative work, and may pay you for the privilege, but the new work is theirs. I do not believe this is normally described as co-created. If you set out to work on the creation together, or simultaneously contribute to the final creation, that would be another matter.
So you might want to add "derivative work" to whatever you've been googling. (And try "co-author" instead of "co-writer".)
"License" is another term to add -- referring to various sorts of permissions people can negotiate with others, in this case to permit the use of copyrighted works.
Licenses can be explicit or implied. Conceivably, if people are posting music in an online forum where it's a free-for-all, there may be an implied license to use the works there to make new derivative works. It sounds like that could be what goes on, from your description. Or there may be an explicit license: Is there a legal agreement or disclaimer at the site? If there is, it should set out the terms for using the site to post material. You may give up your right to control copies made from your works (giving a nonexclusive license to use your work to anyone else using the site). Or it may set out other arrangements. Make sure you read any "terms of use" thoroughly.
2. Regarding the a capella, another member downloads the a capella, loads it to his personal song, and now wants me to sign a songwriting 50/50 split? huh??
I'm afraid I don't understand what it means to "load" something to one's "personal song" in your sentence above. And I'm not sure how your singing a cappella (that is, your voice alone) could be used by someone else in a song he's singing, if that's what you meant. Did you sing someone else's work a cappella? Did another person use your singing as part of a work he or she created?
3. If I use one of these songs in a competition and win something, who do I owe and if so what percentage?
You ask about using the works in a competition and who gets the proceeds... but you need to be concerned about ownership before there's any competition. (By merely performing someone else's work in public it is possible to infringe their copyright, in the absence of a license or fair use.*)
If the work is truly co-authored, then whatever agreement you have with the other author about ownership would probably determine the percentages by which who would get what in a competition--provided the competition related to the authorship of the work.
If the competition related only to how well the singers perform, then I would expect the winnings would only go to the performers.
(*Spontaneously singing "Country Roads" on a trip with friends would be a "fair use". Performing it on a record would require permission from the copyright holder. Talent show performance? probably fair use. Making it part of the repertoire of a professional performer? I'm not sure, plenty of singers have performed other people's songs in local coffee houses without worrying about licenses, but it may be that they were just under the radar in the past.)