I have a question that I want your input on. What does prayer actually do? Does prayer actually change things in the physical realm of this plant? Situations on earth depend on people, and people have free wills. If I pray about someone or something it would depend on someone else making a choice. People can make bad decisions and then the prayer doesn't really work. How would God answer a prayer?
Prayer is a way to worship God that costs you something. In and of itself, it is a part of the battle to draw closer to God as well as that the Lord's will be done on earth. It is also a way to communicate with him, to talk about what you want to talk about and to hear from him if he chooses to convey something. It is a way to show reverence to God. Anything you do with a good heart for the Lord pleases him and also will reap reward eventually.
It is a reverent way to ask God to do something for you or another. It will move his heart if you don't have anything outstanding hindering your prayers, and as a result you have
participating in changing the universe. How he answers is up to him, but at least the fact you took the time, made the effort, and it was to him will be rewarded.
You are very sharp to have recognized prayer that involves another person's will is not the same as (for example) praying for yourself. IMO it affects the power of your prayer. For example a parent's prayer for their underage children is very powerful. If both the parent and child are in agreement in their heart that the parent is in charge even though the child is 30 years old, it is still powerful. If the child has moved out, ignores his or her parent's wisdom, and does as he pleases, then the power of the parent's prayer is much less.
This all has to do with acknowledging God, because all authority comes from God. Coming under someone's spiritual authority forms a relationship that includes God. In fact, not even considering a parent's will or prayer, if the child is obedient to their parent, God's favor will rest on the child. This is also true for obeying the legitimate spiritual authority of a pastor. If a pastor is in such a condition that he should be ejected from that local church, God's hand moves for people obedient to that pastor more powerfully than for those that try to do it themselves.
Having said all that, we are commanded to pray for God's will to be done regardless of the will of who we are praying for. It is God's power that is at work when we pray for a nation's sadistic leader to know the love of God, even if that leader has a heart of rejection for the Lord.
Also, would God provide less then ideal life circumstances because you forgot to pray about something?
The Lord himself may or may not do something different. However, the power of your participation is less. It matters. The rewards of those prayed for go to those who are prayed for.