sop281 : God is All-Powerful, but he wouldn't be Omnipotent (All-Powerful) if he shared power with someone. It would be, this isn't a good example, like a Tyrant, that had a democracy. He can't be a tyrant, if others help/rule for him. Same principle with play4fun's argument. Except I don't want people saying I compared God to a dictator, for he isn't. (That was the only example that popped in my head.) 

If God could create a rock he couldn't lift, he would alter the rock, so he could lift it, if he wanted to. God can create a door, but only if/ when he wants to. But why would God want to create a rock that is "un-lift-able." and are you talking about a "hypothetical" rock he can't lift, or is this something God would really do, in your mind.

I personally think that God could, but he wouldn't. I would have to do more study... Play4fun has AMAZING explanations, in his post above. 

thing1 : God puts us through harder situations in order to increase our potential. I'll use an example that I know you can relate to:
"You were in the Army. They put you through basic training, at basic training they made tasks that would be 'impossible' to the recruit the first time they tried. They (the Drill Sergeants/ Army etc.) created scenarios, seemingly impossible to create the soldiers they needed." 
God does the same to us. He reveals himself to those who are looking. If one is honestly looking, God will reveal himself to you, personally. But, don't let me force anything on you, 'cause that doesn't help me, or you. Does the paragraph here make sense, if not PM me, and we can discuss this outside of the forum. (To prevent spamming.)

darthyoda : Equivalence: the state or fact of being equivalent; equality in value, force, significance,etc.

Omnipotence: the quality of having unlimited or very great power.

You don't simply stop being omnipotent once you have an equivalent being as you still have both unlimited, and great, power. It would simply be shared with the other god. 

sop281: But you do stop All-Powerful. God is both Omnipotent, and All-Powerful. If He created another god equal to Himself, then he would not be All-Powerful.