Firstly, what we think doesn't have any bearing on what was said. You agree it was parable. The first thing we need to look at is who was Jesus speaking to? He was speaking to the Pharisees. We are told in Scripture that Jesus only spoke to them in parables, so that hearing they would hear and not understand. So, His point was to tell them something and yet they wouldn't understand it. Well, they surely would understand it if it was really about dead people. But it wan't. He was telling them what was going happen shortly. The parable is about the coming end of the priesthood and the Jewish leadership. That's why the rich man is in Hades. Hades is the grave. The rich man was a Jew of prominence. He wore purple and fine linen. The priests wore purple and fine linen. The rich man had 5 brothers. Levi, the priestly tribe, had five brothers. Not that long after this parable the priesthood would be in Hades, the grave.
When Jesus spoke of the punishment of the wicked it was in Gehenna, not Hades. John said the wicked would be cast into the Lake of Fire. The obvious conclusion is that Gehenna and the Lake of Fire are the same place. Neither of them said the wicked would suffer in Hades. However, there is a mention of Hades and burning. However, it is not people burning, it is God's anger.
15 But Jeshurun waxed fat, and kicked: thou art waxen fat, thou art grown thick, thou art covered with fatness; then he forsook God which made him, and lightly esteemed the Rock of his salvation.
16 They provoked him to jealousy with strange gods, with abominations provoked they him to anger.
17 They sacrificed unto devils, not to God; to gods whom they knew not, to new gods that came newly up, whom your fathers feared not.1
18 Of the Rock that begat thee thou art unmindful, and hast forgotten God that formed thee.
19 And when the LORD saw it, he abhorred them, because of the provoking of his sons, and of his daughters.1
20 And he said, I will hide my face from them, I will see what their end shall be: for they are a very froward generation, children in whom is no faith.
21 They have moved me to jealousy with that which is not God; they have provoked me to anger with their vanities: and I will move them to jealousy with those which are not a people; I will provoke them to anger with a foolish nation.
22 For a fire is kindled in mine anger, and shall burn unto the lowest hell, and shall consume the earth with her increase, and set on fire the foundations of the mountains.1
23 I will heap mischiefs upon them; I will spend mine arrows upon them. (Deut. 32:15-23 KJV)
We see here that the fire burning in Hades is God's anger against the Jews for their rebellion. Remember, the rich man is a Jew, one dressed in purple and fine linen. He is the one in the flame in Hades. Note also in this passage that God said He would hide His face from them. That's just what He did when the Temple was destroyed in AD 70. The same time the priesthood came to an end, thus the rich man in Hades. That we know this passage is about Christ's day can be seen in the fact that Paul alludes to this passage and applies it to the Israelites of his day. Paul alludes to verse 21.
11 I say then, Have they stumbled that they should fall? God forbid: but rather through their fall salvation is come unto the Gentiles, for to provoke them to jealousy. (Rom. 11:11 KJV)
There's a lot more that can be said on this, but the point is it's not about people being alive when they're dead.
You also referred to 1 Peter 3. If we look closely at the passage and the order of events we find that the proclamation that Jesus made to the spirits in prison was made after He resurrected. Also, the spirits in prison were disobedient spirits, not people, not people's ghosts. They were, what are commonly referred to as angels. His proclamation was that the spirits were subject to Him.
22 Who is gone into heaven, and is on the right hand of God; angels and authorities and powers being made subject unto him. (1 Pet. 3:22 KJV)
So, we shouldn't go around scaring people telling them they are going to burn for eternity. "The wages of sin is death". "The soul that sinneth, it shall die". If people reject Christ they will die. They will be resurrected, judged, and die again, the second death. That's what the Scriptures tell us.