He asks: “How much authority do we have when we say our prayers? Is it okay to feel like we are demanding something?”

This is difficult to answer explicitly because of the limits of language here. When you describe demanding something, if that is expressed in a way that lowers your vibration because of rising anger, frustration, bitterness, or even resentment, this will work against you and your desire for assistance, because we cannot reward being out of divine alignment, so that is not the best way to get our attention and cooperation. Being demanding, like beauty, is in the eye of the beholder. Most people are far too timid to approach us in a strong, confident manner and would consider that being demanding when it is only expressing their birthright, to ask for things and expect a divine response and significant support in the bargain. It is where demanding something crosses a line into blame, and shifting responsibility solely to our shoulders, when there might be a need for you to take responsibility and bear a burden because it is your issue, your need, and your karmic dilemma you need help with. We will not do things for you, but only with you.