Jiinx - we things about your questions (in no order apart from the order they come into my head!!) ...
.. the sleeping bags are called GroBags (thats the company who started them) and are fantastic once they stop being swaddled
... babies rub their eyes and pull at their ears when they are tired which is probably what she is doing
... my DS used to be a nightmare to get to sleep but now he can roll he likes to sleep on his side (and I wonder if he would have slept better when young if we had done that)
... I know they recommend sleeping on their backs, but when I was small they recommended sleeping on tummies, and it changes from time to time
... think once they learn to roll a bit they do tend to end up in funny positions (DS is almost 9 months and still does!), that is why grobags are so good as they are still covered and blankets dont go over their face, etc
.. at your DDs age they don't really like their tummy as their heads are so heavy, but over time they find it easier. My friend bought something to lie her DD over to encourage her to lift her head, etc but it was a waste of money .. when they get stronger (and more in proportion) they do it naturally! As long as she doesn't spend all day on her back it is fine (sure you will have her on your knee, etc lots so her head will be fine!)
.... my DS stopped being swaddled as he used to be so strong he always broke out of them so had to just stop. He used to flap like mad going to sleep (even if dozing on me, then laid down) but he was 4 months so I used PUPD with him (with advice from forum, of course) and I stopped being a prop to get him to sleep (he would then waken up lots in the night as I was cuddling him to sleep so he expected me there whenever he woke) and he started sleeping well again.
Finally, you will get there! I used to never get DS to sleep during the day without sooooo much stress but now he just lies straight down and falls asleep (which I thought would NEVER happen)!!! Just think, when they are teenagers they wont ever get out their beds!!!