So Jonah soul is in Sheol?
It was for a period of time.
Is this hell?
No, Hell is the lake of fire, conclusively proved by @Nehemiah6 here. Thanks Nehemiah
Is this not the same place the rich man was?
Sheol/Hades is where the rich man was.
Your doctrine is a bit confused...
No it isn't. Stick with it.
Did Jesus preach to the spirits in prison?
Yes
Did the bible speak this prison is in Sheol?
Yes. There was a separate location here called Paradise (Abraham's Bosom) but this is no longer the case since the resurrection of Jesus.
Who are in this prison?
Fallen angels, Nephilim, as well as the souls of unrighteous men and women.
1Pe 3:19-20 KJV 19 By which also he went and preached unto the spirits in prison; 20 Which sometime were disobedient, when once the longsuffering of God waited in the days of Noah, while the ark was a preparing, wherein few, that is, eight souls were saved by water.
Disobedient during noahs days...
Yup. Even before that. It would have been populated when the rebellion happened in heaven and one third of the angels were cast down. Sheol was created for the devil and his angels. Some are currently in chains there, whereas others are free to roam about the earth, as agents for temptation of mankind (just as Eve was allowed to be tempted, so mankind is allowed to be tempted).
2Pe 2:4-5 KJV 4 For if God spared not the angels that sinned, but cast
them down to hell, and delivered
them into chains of darkness, to be reserved unto judgment; 5 And spared not the old world, but saved Noah the eighth
person, a preacher of righteousness, bringing in the flood upon the world of the ungodly;
See previous paragraph