Rodger. I will try to answer then to the best of my ability, I believe everything to be accurate but I may be wrong or out of date.
1.Duoing in Solo does affect mmr, it adds a bit extra to your team as the system values premades to be stronger then just solo. So if your say 5 and your duo is 3 you end up with 9 or 10 instead of 8.
2.You gain MMR for every win, you lose MMR for each loss. LP is affected by your mmr, the higher your mmr to division the more lp you get, vice versa. Beating teams that are slightly favored gets you more MMR and losing when your favored cost you more MMR. Win streaks might have a hidden extra mmr bonus, or alternatively you just end up with mmr above your division so each win counts you as unfavored and thus your mmr spikes. Riots quite on this one. End result, just win a lot to raise your mmr. You can lose lp from decay, or from dodging lobby but it will not affect your hidden mmr.
3.Far as information, I don't work for riot so this is just imo. But my guess is a combination of that they don't want it to get abused, and odds are they don't want to make it public as all the work they do on this system then could be used by their competition for free.
Sources in addition to the ones I used Old boards Plus a few pages that no longer seem to exist.
Edit. I was on the fence about shareing this link cuz I dislike boosters. But here is some boosters website that has some info, admittedly they are trying to sell themselves and take your $ so take it with a grain of salt. Don't pay for a boost ever please. you don't get any better just learn to improve dammit.
