If you win you'll increase, if you lose you'll decrease, it's pretty simple. As you have >50% win then you'll probably win some and increase, come up against better players and level out.
You can only check the MMR of your friends or if they have a team you can see the MMR of the team on DotaBuff.
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i have a win ratio of about 56% for my solo MMR. I rarely play rank game because i don't find myself enjoying the game as much. Could i increase my MMR rating or would i just lower it if i play rank? I stared out with about 3800 MMR solo rating and almost hit 4100. Is there a way for me to check other people MMR rating too?