I was wondering about MMR

So yesterday I was playing normals with a friend like we do whenever we have free time. I am currently Gold 5, where I ended last season, and he is Silver 3. Now, when I play Ranked I sometimes play with low Platinum people, other than Gold and Silver. So yesterday at the end of a close game that we won, I went on LoLKing and looked up the enemy team; turns out they had two people from Plat 4, two Gold 3, and a Silver. Our team had one Gold other than me, and others were Silver.

I was pretty happy that we were able to beat them, considering their much higher division. I don't play lots of ranked, because it is kind of stressful sometimes, and I was pretty confident that I could climb some more, but this made me even more confident. Looking better it seems that lots of the matches we play have Plats in the enemy team, and that lead me to thinking the MMR system must "think" we are higher skill than our division would indicate.

However, whenever I look into the whole MMR thing I am always very perplexed about how it actually works. I heard that Normals MMR and Ranked MMR are independent. But how are those calculated? And why is it that even though we play versus people much higher division our teammates are actually mostly Silvers? Does the system make random teams, or does it try to balance it in any way?

But most importantly, something that I've always wondered is this: why is there a need for Riot to separate MMR from your League Division? I mean, they say your division reflects your skill, but if they believed in the division system they created, why do they need a separate parameter to determine your skill for matchmaking? And why do they keep up from knowing our own MMR? It is like if they didn't have faith in their own Division system they created... and also I really dislike the fact that they are not disclosing our personal ratings and how those are calculated and what they do. I mean, why can't we know?

Anyone that knows any facts about MMR, let me know down here, I'm very interested in understanding it better. And wish me luck, seems I'll be trying for Plat this season :D