It is quite clear that you do not understand most biblical doctrines.
What is clear that I do not understand the interpretation that you place on them over and above that which was given to us by the Holy Spirit and Christ to the Apostles.
"-Paul says we are "dead" Eph 2:1-3.
Yes, context is everything again. Don't pull this out and forget where he separates unbelievers from believers in the rest of the whole chapter. In fact, in light of your statement above, he includes Isreal as well. Christ broke down all walls between men and Himself. He did that in His redemptive work. All mankind.
-Paul also says there is no one who searches after God or even does anything good. Rom 3:10-12
He is answering the questions that are rasied by the hypothetical Judiazer he is addressing in the first 9 verses. Then He goes on to build the argument that it is not of our perfect righteousness which he just described as none, but the mercy of God saved us by Grace. We do not need to fulfull the law perfectly because it is an impossibility, but Christ did so for us. We are saved by Grace through faith, not anything man can or could do. vs 27 summarizes what it has always been in OT and NT, the law of faith.
-Paul says were at enmity with God and cannot please him Rom 8:7-8
Yes, those who are not of God. If those who live by the spirit, those that chose to accept Christ, since with the redemption of man, all men are once again able to chose to walk with God. We must put the body to death and let the spirit rule. If we do so we walk in the light. If we chose not to so walk, then we are children of darkness. This choice is only possible because it was not limited to only some.
Jesus even says we refuse to come to him. Jn 5:40
No, not necessarily. He is speaking to the Pharisees. They do not come willingly so that they may have life. They rejected the God of Isreal, now they are rejecting the Messiah. There is nothing here to show either side of redemption, except that Christ clearly implies choice. Cannot be decreed election either.
-Jesus says we are children of the devil and it is OUR will to do what he desires. John 8:44
Precisely, it is our will that makes the difference between believer and unbeliver. If one is willing to believe, he is also willing to listen. Again, choice is spoken and implied. Choice is not even a possibility with limited redemption. Vs 51 is also a choice, not decreed election or limited redemption.
-John 8:36 So if the Son sets you free, you will be free indeed.
Yes, mankind has been set free. Free from the bondage of death and sin. Free as in the pre-Adamic state, that man can once again chose, as did Adam, to either love and obey God or chose to reject Him. Man cannot be responsible for that simple decision unless God redeemed all of mankind so they can be held accountable.
like SemperReformanda said only if God draws us or enables us. Jn 6:44,65
Yes, except that calling is specifically in Jesus selecting the Apostles, whom He already knew by His foreknowledge they would believe. Peter bears this out in the following verses. Better verses which are in context to what we are speaking about is: II Pet 3:9, Rom 2:4, Mark 2:17, parallel Matt 9:13, Acts 17:30, It seems that God calls sinners to repentance. Now, either only a few are sinners, or God is in fact calling all because He freed all from the Bondage of death and sin. Or, you have a different meaning of the word "all".
- John 1:12-13 says But to all who did receive him, who believed in his name, he gave the right to become children of God13who were born, not of blood nor of the will of the flesh nor of the will of man, BUT OF GOD.
Yes, we could not even recieve Him nor believe Him except that He redeemed us. He redeemed all, so all could have that choice. A choice man will be held accountable for at the judgement. If this is not so, then either some men will not be judged, or man is not accountable and no one is judged. Some clear contradictins you are creating in attempting to skirt around universal redemption.
-Phil 2:13 for it is God who works in you to
It is all God, no matter how you look at it. However, God will not impose His will on man. Man must permit God to become part of His life. He choses to believe and since all men have that choice, then all must have been redeemed.