Your MMR is calculated by your wins/ loses and what ranked you were at the previous season I believe. My question is, does your MMR fall if you dodge a queue for whatever reason when you lose those 3 or 10 LP after you've left?
No your MMR does not drop and it will also not decay from inactivity. Really the only things that affect your MMR are winning and losing. Up until last Season Queue Dodging was used to "troll" the League system by playing into a promotion and then winning one game while dodging the other one. With this trick players were able to reach Diamond MMR while being placed in a Bronze league.
Basically, if you dodge you will lose LP but you will gain slightly more LP next game.
First of all it seems you may have some misconceptions on MMR. It is not solely calculated based on your wins and losses. There are other factors that are taken into account. Now the specifics will be dependent on the implementation of the specific system that Riot decided on. But in general there are several factors determining how much MMR you gain or lose.
The first factor is the MMR of your allies and your opponents when you win or lose. For instance if your team has a lower MMR than your opponent if you win you will gain more MMR than if you had a higher MMR than your opponent. Note that teaming up with friends in the dynamic queue is also likely to boost your team's MMR.
Another factor is what is known as 'uncertainty'. Which is a measure of how sure the system is that the MMR for you is correct. Uncertainity is higher when you haven't played many games (this is part of the reason why you need to play 10 promo games before being placed into a league). Or also when you haven't played much for a longer period of time. Although I cannot be sure, but it is likely that dodging will increase your uncertainity factor but not directly change your MMR.
no it won't , But if you dodge 4 times in 1 week , you can get ban for 1 day cause i did . Dodge 2 times in a row , 30 min ban from playing. And heres a fun fact , if you dodge in your promos , you DONT lose your entire series lol