CONSOLIDATED VERSION
A (not so) small introduction to better contextualize some of the following questions.
What we experience in everyday MM: we reach a certain "personal score evaluation" (I'll call it "elo" for the sake of brevity and also because we can have an idea of our real MMR only by third site calculations), let's say 2000 elo, just for using a number easy to remember, and a high player level, again let's say level 100, and then we find ourselves in "strange" games. We are matched with level 31 players, or 1400 elo players. On top of that, against 2700 elo players. Also on ranked, we find ourselves matched with people of very high/low rank, if compared to ours.
We also experience that, after a winning streak (maybe AGAINST very low elo/level players), the number of super low elo/level players in our team raises. This will lead to two scenarios: 1) we have to super carry the team, in order to win or 2) we lose.
Being this a team game, we'd like more balanced teams to play with and against. As Epplz has shown in the MM conundrum thread, the percentage of easy games (elo gained around 5 points, elo lost around 20 points) is very low, the percentage of balanced games (elo gained/lost around 15 points) is low, the percentage of hard games (elo gained around 20, elo lost around 5 points) is very high. This "spread" leads to very unpleasant losing streak. It is not a matter of "we don't like to lose", which is normal, it is a matter of "we don't like to lose because we are in games impossible to win". It is even more frustrating when getting most eliminations/dmg/healing/best streak/most obj time/whatever, and then lose points due to a poor performing team member (or, even worse, a disconnected ally). We can't do anything for connection problems, but MM can be improved.

What your previous Q&A seems to suggest (very simplified version):
If NewPlayer real elo is 2000, the system starts to "test" him putting him with and against 1500 elo players.
If he wins, his new supposed elo is now 1600.
The system now puts him with and against 1600 elo players.
If he wins, his new supposed elo is now 1700.
[iterations]
The system now puts him with and against 2100 elo players.
If he loses, his new supposed elo is back to 2000.
He would now play with and against around 2000 elo players, till he improves at the game and wins several games, in order to reach 2100 elo players.
At this point, a balanced system tends towards the 50% win rate, because the 2000 elo players is facing half of the time around-2000 elo enemies a bit better and a bit worse than him.
This is good.

What we actually see in game:
NewPlayer experience a streak of random matches where he can find very high and low elo players both in his or in enemy team. The spread is so crazy, he cannot recognize an "improvement path". Moreover, after finally reaching somehow his real 2000 elo, he then finds himself stuck in games against 2700 elo players, but with a total newbie of level 31 and 1400 elo in his team. And we all know that, in this situation, we are simply playing 4vs5, even if the newbie is actually doing his best (by the way, this also leads to a general toxicity increase towards the newbie, which is not fun).
In this scenario, it seems that the 50% win rate is obtained by forcing very bad players in NewPlayer's team, as soon as he's able to enter a winning streak. It seems that the 50% win rate is FORCED in this way, and this is not good.

Hope this introduction would be helpful in contextualizing some of the following questions.
And now, let's go with the questions (additional comments in the square brakets). Credits in the threads and in some PMs I've received. Please, keep in mind I am trying to "summarize" some of the similar questions, or questions that have been asked more than once.

QUESTIONS
  1. Why the MM system of Paladins has not been published? Smite one is public (ie: Guru is based on it), so why not showing also Paladins one? Can we see the actual formulas used to calculate MMR, TP points and rank-skip?
  2. Why you aren't publicly showing the MMR? [Somewhere you said it was for limiting toxicity, but this is unlikely to happen: people are toxic on ranked borders and even on Guru scores, so... Showing real MMR would, at least, make people going toxic over real data, and lead to a better evaluation of MM]
  3. Why the system does not evaluate also personal performance? [From previous Q&A it seems the system only evaluate against who you have won/lost. This lead to the incredible frustrating experience of losing TP points and MMR also when being the best player in the game, just for an ally under-performing or going afk]
  4. Is MM evaluating also the personal performance related to a specific champion? [winning with my main is easier than winning with my worst champion and... when I play with my main, I am ie: 2500 elo. But when I play with my worst champion, my elo is far lower. Is the MMR gain/loss considering also this?]
  5. Are you going to modify the MM (and relative MMR gain/loss) in order to keep trace of personal performances?
  6. Keeping in mind the "(not so) small introduction", is the introduction of lower elo/level players in a higher elo/level team a way to achieve the 50% win rate? And if somehow true, would it be possible to use a smoother approach to make the model converge at 50% in the end?
  7. Do you plan in separating the queue in the future to avoid parties vs solos and parties abusing the system?
  8. Regarding Casual queue: which is the rule for finding a game to full pre-made parties? [we have seen average full pre-mades get matched against pro players. Pro players full pre-mades get matched against average players. Both resulting games are stomps and, on top of that, it seems that MM is not consistent about full pre-mades]
  9. Having a high win rate seems to result in getting lower and lower win rate allies. Is this actually a thing? And if so, is it beneficial to get a minus winrate so MM will set you with better team member?
  10. About ranked, on the base of what the "skipping rank" is decided?
  11. Does MM take into account the number of reports a player got?
  12. How does being in a party affect MM?
  13. How long does it take in queue before MM starts to lessen the "balanced team" requirement, in order to find a match?
  14. Does the MM try to match players with similar pings?
  15. Does the MM try to match players with similar levels? [if there are some "categories", ie: levels below 30, levels between 31 and 50, and so on, we'd like to know them]
  16. Does the MM try to avoid putting players with the same main champion on a team?
  17. Does the MM give more or less rating against different enemy team compositions?
  18. Why is Competitive and Casual MMR fully separated? [A Grandmaster that doesn't play Casual will have a very low Casual MMR, but s/he would still be super good at the game. So, putting him/her with and against low MMR players is greatly unbalanced]
  19. If Diamonds can't party with gold and lower rank players, why they end up in team with low rank players?
  20. Does MM match you with players you have blocked?


    BONUS QUESTION
  21. If HiRez would put online the new card system (and we all hope it wouldn't!), will MM try to match players with similar average card-level?


Thanks for your attention and the possibility to get these answers, from me and the whole community!