If philosophical discussions and debates such as these interest you, then you should begin studying the field of Christian Apologetics. An excellent author to begin with is Ravi Zacharias.
As far as having answers, if indeed the Spirit of Christ is within you, then do not worry about having the right answers. Offer your mind and thoughts to Jesus freely for His use. When the time comes, He will give you every word you need to say.
As for your request, I will try to help by providing some refuting arguments to His article. Though, as you said, it will be long. I will break these up into the different sections the writer has established. You will need to read what the write wrote first, and then follow with my responses. Here goes:
The theodicé problem
Indeed, the author's thinking is correct. God cannot be almighty if He is limited by any characteristic or trait. God is indeed greater than all things. Christ said, "All things are possible with God." This means God has no limitations. He is not even limited by good or evil.
However, God is good. So how can we say both? Quite obviously, because God chose to be good. He chose to limit Himself. The way God did this is by giving birth to a Son. In God's son is the embodiment of all that God is. In Hebrews 1:3, it says that the son is "the exact representation of His nature." Though all things are possible for God, He chose His Son to be the representation of His nature.
The ontological evidence against gods
There are two reasons why God does not answer prayer, and why this reasoning fails. 1) A person prays to the wrong God. 2) The person is not in a right relationship with God. If a person has wronged God, why should He answer?
If a person approaches the throne of God and has not been reconciled of sin, God would have no choice but to execute justice. When God does not answer a prayer, it is out of mercy.
The meaning of the word existence
God gives existence to all things. God is the unchangeable "I AM." However, everything else changes. Everything else is variable. Because God never changes and is always the same, everything else can have a basis for existence.
God has given of Himself to provide existence to all things. We exist because God exists. If God did not exist, what basis would we have to exist? Could we even say that we exist?
God is not merely the reason for all things, but a necessary reason. Many people in the field of science say that God is not a viable explanation. However, what many in science don't realize is that they need God or else science becomes obsolete.
The entire basis of science is math, logic, and experimentation. A scientist studies the universe looking for explanations of how it works. What a scientist discovers is natural principles at work governing the universe. This natural order is measured in the language of mathematics. The entire universe follows this language.
Within the universe is a certain rational. The scientist goes about studying on this basis: that everything has a logical explanation. We can say everything has a logical explanation because the universe is based upon God's Word which is filled with wisdom (logic and reasoning).
If the universe were random, then we would not expect everything to have a logical explanation. Rather, everything would be random. A person may ask, why does an apple fall off a tree. In a random universe, the answer would be: "because it is random." However, science does not accept such a proposition. Science says, "There must be a reason. The reason is gravity."
And so, science needs God as the basis for all reason in the universe, or else science is obsolete. All things merely occur randomly.
Some things are impossible to do:
God set forth His Word to be the supreme authority governing all things. His Word bears wisdom. It has a particular logic that governs all things. We can easily see through science that all things follow a particular logic. This has been established by God's Word.
Indeed, there are things impossible to do. This is because God has established His Word as the supreme authority over all things. God's Word is absolute and does not change.
However, God is greater than His Word. His will always be greater than His Word. He is in control of His Word. This means that if God wants to walk on water, He can do so freely. He is the one in control. There is no contradiction here.
Omnipotence is impossible due to paradoxes
Free will is not free choice. God has given free will to men. However, God has not given men the freedom to do whatever they want. Inside, we may want to fly, however, does that mean we can fly?
Many people confuse free will with free action. We do not have free choice. We have free will. We have the freedom to believe whatever we want.
We would never notice god
Again, the problem here is that the author does not know about God's Son. God is above and beyond all things. He is greater space and time. Being this is true, how then can we know God? If God does interact with the world, like he says, then God would change all things, not one thing.
God gave birth to a Son. This Son is the image of God. Though this Son, we may know God and interact with God.
As far as prayer is concerned, the author doesn't know the purpose of prayer. We do not pray to God in order to influence God. God does not change and if He changed according to our desire, the world would be evil just as we are evil. Rather, prayer is about being united with God as one. When we pray, we are to pray "in the name" of Christ. When we pray, we are sharing in the person of God. We are sharing in all that God is. We are asking God for things He has already planned on giving us. However, He desires that we be a contributor so that we might have faith in Him.
The author says, "Do it yourself." However, this is an ignorant statement. The author is telling people to act in ignorance. God knows all things. We only know what we see through our narrow vision. We cannot possibly know all the ramifications of our actions. However, if we pray to God and allow God to work in us, then God can control us. This means our actions will be based upon God who is supremely good and knows all things. However, if we act independently of God, then we will most likely cause harm. Hence, why the earth is suffering from things like global warming. The earth is dying because humans have acted independently relying on themselves rather than God.
Nobody really believes in god
Faith that is blind is no faith at all. When we are a child, we might believe in Santa Claus waiting all night for him to come. When he doesn't show, we realize our faith was false. As such, we never had faith to begin with.
My faith is not dependent on me. In many religions, people believe in God because they believe. Their faith is dependent on them. Just like the child who believed in Santa Claus. All faith needs to have evidence. Even the writer of Hebrews said in verse 11:1, "Faith is the evidence of things unseen." True faith is not blind. True faith has evidence.
The Christian faith is based upon a God who saves His people from their sins. The work of Christ in the lives of sinners is the evidence for faith. When we call out to Jesus to save us from our sins, and He does save us, then our faith is proven.
My faith is proven. When I called upon Christ to save me, He saved me. I was a smoker, drinker, fornicator, blasphemer and more. I was suicidal and depressed. Christ changed me. I no longer do any of those things because Jesus saved me.
There is reasonable cause to believe in God. In fact, it is more reasonable to believe in God. Anyone who says there is no God will have to face death. There is no athiests in fox holes.
For anyone to say there is no God is only foolishness. A person says there is no God because they want to be in control of themselves. They want to be their own God. They don't want to be saved. They like their sins. They want to do things their own way, not God's way. And sadly, they will realize that God has reserved a place for them where they will be independent of God.
If anyone wants a reasonable cause to believe in Jesus Christ, look at the condition of humanity. We need help. We need a savior. We are hopeless. We need a God who can redeem us and make us new.
These are some short and quick answers. I hope they help.
Your brother in Christ,