Before I continue this lovely discussion (which I am thoroughly enjoying), because I am entering dangerous territory now: I just want to make it clear that I am not not trying to push any belief/faith on you. There are of course, many definitions of a God, depending on which religion you choose from.
These points are made by taking basic (and some complex) concepts of God and comparing it to the subject anime character in question.
I disagree with your point that her final form is omnipresent, omnipotent nor omniscient.
Okay so maybe not omnipresent...
Moving on:
Madoka wishes to destroy all the soul gems no matter what: that it can be seen as omnipotence. Why? Because that is an impossible wish in the current state she was in and she had to be given the powers to do so.
One would have to either go into a God-like state or become a God to even remotely come close to moving through past/future freely. That would not make her omnipresent, but it does make her immortal which means she is always there, but not everywhere at once, but again, God is, in a way, immortal. She is also going around releasing magical girls from the timeline (from first to last). When one changes the timeline, passive or not, they are essentially creating a different world (another display of omnipotent, how much power do you need to change the world as Madoka did is probably debatable).
Now for those options that were never portrayed:
Her powers were given to her to preform the function of her wish. One would think that would make her limited, and of course it does. Madoka can't do anything other than what she was made to do. Even if she wanted to be with her friends she couldn't. That is not the purpose of her powers. She can't do anything outside her function, but that doesn't make her not a God.
Well...God has a function if God goes against his/her/it's function, then wouldn't that defeat the purpose of having one? Check links to get a better explanation of this.
So for your points:
-preventing all misery ever from happening (or for a specific one: at least her friends from dying)
-solve the universes energy problem which made Kyuubey scheme necessary
- ban Kyuubey's existence
- give herself a physical form and live her life together with Homura
These can easily be explained by the fact they are not a part of her power's function, so she can't preform them. If her function wasn't a factor let's take these into consideration:
-That first one: God doesn't always do what's best for others, if things are meant to be they are meant to be. Simple as that.
-See above.
-Banning Kyuubey's existence before any of this happened, would be problematic. There would be no such thing as witch/soul gems to begin with, thus Madoka wouldn't have been able to make her wish, and that would just defeat the purpose of the show.
-Let me ask that question with another: if God (once again depending on what you believe) is all powerful why doesn't he/she/it do that to prove he/she/it exists? Either God can or can't is debatable and so is Madoka's ability to do so.
I said my piece on the subject matter so I won't continue after this post cause ohmygod if I continue on like this I might get carpal tunnel.
Some sources to help get my point across:
Webster definition of God: http://www.merriam-webster.com/dictionary/god
Wiki definiton of God: https://en.wikipedia.org/wiki/God
Madoka's wiki (for her wish): http://wiki.puella-magi.net/Madoka_Kaname
Some blogs to help my point because they are more organized than my thoughts: http://animemoonblogger.blogspot.com/2012/06/transcendence-of-kaname-madoka.html, http://brianandrew.wordpress.com/2011/04/26/madoka-magica-eleven-twelve-madoka-becomes-a-god/
