You are saying that we die once, and you mention a death that comes when we sin. If that is a death, and we also die physically, how is that not 2 deaths?
What we call physical death is illusory. The only real death is separation from God. Jesus said you will never die if you believe, and have no life in you if you don't believe. If you can never die, then you only died once when you became a sinner. The wicked only die once, for the same reason you died once. The "second death" is figurative for the destruction of the wicked; it's called the second death to distinguish it from the illusory (first) "death" Jesus called sleep.
Or are you saying none of these passages are about physical death?
The second death is annihilation, unbelief resulting in the loss of body and soul on the Day of the Lord. Physical death is illusory, the living spirit simply returns to God and the body returns to dust; it's described in a number of scriptures as sleep.
Also, what judgment do you think is mentioned in Hebrews 9:27?
It is the Day of the Lord.
2 Peter 3:6-13
6 Whereby the world that then was, being overflowed with water, perished:
7 But the heavens and the earth, which are now, by the same word are kept in store, reserved unto fire against the day of judgment and perdition of ungodly men.
8 But, beloved, be not ignorant of this one thing, that one day is with the Lord as a thousand years, and a thousand years as one day.
9 The Lord is not slack concerning his promise, as some men count slackness; but is longsuffering to us-ward, not willing that any should perish, but that all should come to repentance.
10 But the day of the Lord will come as a thief in the night; in the which the heavens shall pass away with a great noise, and the elements shall melt with fervent heat, the earth also and the works that are therein shall be burned up.
11 Seeing then that all these things shall be dissolved, what manner of persons ought ye to be in all holy conversation and godliness,
12 Looking for and hasting unto the coming of the day of God, wherein the heavens being on fire shall be dissolved, and the elements shall melt with fervent heat?
13 Nevertheless we, according to his promise, look for new heavens and a new earth, wherein dwelleth righteousness.