Does the soul of unbelievers survive the second death?

BORA - It does seem fairly clear that God spoke directly to Adam, Eve perhaps even Cain and others. Speculating (which is what we do a lot of here) is okay, just do not go down the rabbit hole to far
Gen 3:13 And the LORD God said unto the woman, What is this that thou hast done? And the woman said, The serpent beguiled me, and I did eat. 16 Unto the woman he said, I will greatly multiply thy sorrow and thy conception; in sorrow thou shalt bring forth children; and thy desire shall be to thy husband, and he shall rule over thee.
Gen 4:6 And the LORD said unto Cain, Why art thou wroth? and why is thy countenance fallen?
Birds and fish were on day 5, land animals day 6 with man after the land animals. Gen 1:20-26

Noah was on the ark for about a year. As reepicheep states (a tad incorrectly) they couldve brought eggs on board the ark, however that is slightly inconsistent with Gen 7:9 but I wouldnt be dogmatic about all the animals going into the ark as I would have to ignore Gen 7:1-5 where the instructions are given and verse 5 states Noah carried out the command of the Lord. Reptiles lay eggs and take anywhere from 1-4 years to reproduce. It is not a stretch to think that if not eggs were brought on the ark, the animals were juvenile just prior to reproductive age and upon exit of the ark they became reproductively active. The pictures in childrens books of Noahs ark are cartoon like and should be treated as such. Full grown elephants, hippos etc. were highly unlikely on board the ark

Let me give you an entirely different perspective on this. This is the short version. 

Read what is written in Revelation 20:


So Death and Hades (Hell) give up their dead, then it is Death and Hades that are cast into the Lake of Fire. Is the Lake of Fire a term for Hell? Can Hell be cast into itself?

Annihilationism essentially 'eternal death', which contradicts 1 Corinthians 15:26.  

What is the "Lake of Fire" then? If you look at the historical understanding of that phrase, it's something that Dante (where we get much of our theology of Hell) got wrong. The term was used by ancient writers to describe an actual physical place that at the time had a lot of seismic activity. It has calmed down so much that we today call it the Dead Sea. Back in the 1st Century and earlier, it was a place of fire where people who wanted to cast away things forever so they no longer had any influence in the world - idols and useless things.

Also, the word "torment" is the Greek word for a touchstone that was used to test gold and precious metals. It's not torment as medieval fiction writers envisioned it, where the God of love actively subjects people to the worst physical pain imaginable for eternity with no hope of forgiveness (contrary to Matthew 18:21-22). BTW Read Revelation 14:10 - people will be "touchstoned" in the presence of Jesus and His angels. It's a test of genuineness and "the inner conviction one feels when they are presented with something contrary to their nature".  "Fire" is used in the Bible as a picture of judgement and conviction. Like when we say someone was "burned" in a mocking way.

So God does not actively subject people to eternal conscious torment. What essentially will happen is that unbelievers will become aware of the full presence of God and have internal conviction about how short they come to His glory, because they don't have the covering of faith in Jesus. They may also dwell in eternity somewhere outside of the presence of God. 

This is the summarized version, a more detailed analysis of this perspective was written here.