If you believe that you can come to Christ independent of the compulsive influence of the Holy Spirit, then you are flirting with Pelagianism. God must (one way or another) make you willing and take away your natural unwillingness to repent and believe. It therefore requires a supernatural act. If you believe you did it on your own, then your salvation is the result of a natural act.
Is believing the gospel irrational?
It is both unnatural and irrational. No man who is uninfluenced by the direct intervention of the Holy Spirit will ever make a rational decision to embrace the gospel of Christ. If, at the time you received Christ, you believed it to be a rational decision, it was only because the Holy Spirit put the ability to see that as a rational choice in your heart. It didn't grow out of some kind of natural tendency in mankind. The natural tendency of mankind is to reject the Gospel, as it makes no sense to the person who is not under the direct influence and guidance of the Holy Spirit.
Now that belief is a work. You had to work hard to come up with that conclusion
No, your answers were classic Pelagianism. Even Arminians would refute them.
Another typical Calvinistic refrain --- and you think that classic Calvinism is biblical???
Already today we have discovered that the Calvinistic claim that "believing" is a "work" is unbiblical. How many more of its invented doctrines are as well?
Show me from scriptures where faith comes to anyone before or apart from the word of God.
Show me from the scriptures where one is regenerated [born again] before or apart from the gospel, aka the word of God?
I won't hold my breath ---
I think you would find Jonathan Edwards on the "Freedom of the Will" to be very enjoyable. Edwards is great because he is brilliant and a wonderful theologian, yet he is not some abstract theoretical guy. He wrote most of his stuff in the middle of a mind blowing, Spirit drenched revival that literally shook the hinges off the church doors. We have never seen in our age something to compare. He is a theologian of the heart. We could stand some more of what followed his ministry. His theology ain't bad, either.