Hi Believer. This is wise of you to seek understanding in these things as a new believer. I hope you read something in your Bible today and prayed to the Father in Jesus's name also. It's good to do this first, sometime in AM before you get the day going as this way you put God first and have his blessing for the day.
Having said the above, to get to your questions, lots of Christians, including some with divinity degrees have erroneous ideas concerning the trinity. I did a trinity thread here in one of the forums some time ago. Possibly a search of it would bring it up.
Go to the Bible for your answers.
1. Jesus always referred to god the father as "Father", or "God". On the cross he called him, "my God." In John 14 he said that whoever has seen him has seen the father. This is a qualified statement, because later in the same chapter he said "my Father is greater than I." How can this be? What he first meant is "if you've seen me, you've seen what my father is like. The second statement he made was in the sense that the father is always greater than the son. He came to do the father's will.
2. The apostles in the New Testament books called the epistles (most of these follow the 4 gospels) always began their letters with something like "from God our Father and Jesus Christ the Lord." This means the father is the god of us and Jesus is the lord of us, or our master.
3. Jesus is the mediator or the way/ambassidor to get us to God. That's why it is important to pray to the father in the name of the son, Jesus. Jesus taught us this in the Lord's prayer when he instructed his desciples to say "Our Father who are in Heaven." He also taught this in John chapters 15 and 16. Read those.
There is a literal heaven where there is a literal throne where God sits to govern/manage the universe. After the resurrection, Jesus rose to sit on the right hand of God. You're right, he didn't sit in the place of God. He's on his right hand. So they are separate, in that one is the Father and the other the Son. They have different functions also.
How is God the father and Jesus the son one? They are one in that the spirit of them both is the Holy Spirit. That's also why we can call god Father, because when we receive Jesus as saviour, his spirit and the spirit of the Father comes into our bodies, souls and minds. We then become the children of God.
Don't expect to ever comprehend or totally understand the Trinity, but here are some Biblical givens for your and other readers to ponder.