To your first question: Riot replaced an open elo system with a division system so people felt like they were progressing and to avoid direct elo comparisons that always arose.
To your second question: Riot will probably never release the exact calculations or numbers.
To your last comment: Riot has no incentive to make a broken, unfair system. It will have bugs and glitches but eventually you will settle at the place you belong.
Thank you for the direct reply to my questions.
I definitely feel at this point that there is no progression, whereas I was steadily rising in the elo system. However, I realize most others are able to progress quite easily and quickly so they seem to get upset when someone questions whether everything is working properly. I've seen screenshots of people losing LP for winning games, so yes, there are obviously some things not working at the moment, I was just phishing for more information regarding my personal experiences with the new system.
Coming from a competitive gaming background I find it hard to believe that they really haven't/aren't going to release information on how their 'ranked/competitive' system works. It seems like there would be no reason why they should keep it hidden, since it only keeps people from knowing where exactly they stand. I assumed that someone would have figured out how it works already, but maybe those who know don't browse these boards, or if it's only riot employees who know, perhaps they are under some nondisclosure thing (who would know for what reason, but still) that is keeping them from discussing it publicly.
Thank you and thanks to everyone else who replied and tried to help. I guess it will take more time for the information I'm looking for to go public.
A mod could close this now or simply let it die.