you don't need to read so much versions of the Bible, though. i don't know how to explain God logically, because, i'm only like 13 years old... but i'll try.
all the other gods are crafted by the minds of humans, but that idea came from their knowledge of the real God. they just wanted a new name, a new identity, or an idea of what God really looks like if we can see him. i know a bit of Islam coz we study it in history. Muslims say Allah is just one of God's names. Christians call God Jehovah or Jehovah Nissi and a lot more names. icons like Allah and Buddha is just an imagination of what God looks like.
do God exist??? yeah, He does! there are a lot of ways to prove it. whenever there's something bad happening to you, that doesn't mean he doesn't care for you. instead, that's his way of testing you if you believe in him, especially in bad times. that's what happened to Job. God gave Satan permission to make him suffer, so he can see if Job will still cling to his faith in bad times(because Job is so blessed right??? he's got every riches in that time. God just wanted to see if he's still gonna thank and praise Him in bad times).
whenever someone's bullying you or stuff like that, just let them do what they want to do, and i tell you, God will punish them in a 'special' way.
whenever you're doing some office work and you suddenly forgot what to do, just utter a simple prayer of help and God will help you, IMMEDIATELY!!!(i've proven that lots of times)
if you're really in doubt, just ask God to help you understand Him.
but you know, i don't know how to explain God logically...
He works in ways we cannot see. He can be right beside you in bad times. He hears millions and millions of people at the same time. He forgives our sins whenever we ask Him to.
i think it's His love for us, not logic...
*just ask God to help you, and He will. He always does, but remember, God wants us to learn how to be patient. He's got 3 answers to your requests: Yes, Wait, or No. He knows what's good for you and He will make you see it, so don't get mad whenever He says no to you. He said no to me a lot of times through my parents and he makes sure that they make me see what will happen if i had that or if they allowed me to go out with my friends.*
so i guess my answer's not logical, but i did my best to explain Him in a logical way... c",)
i wish the best for you and your adventure in understanding God logically!!!