After being saved or not being saved but repenting, are you still punished for your sins and is it possible to not be saved and repent?
Certainly there is no forgiveness without repentance, but you know that. That is not your question. Your questions are whether repentance prevents punishment and whether repentance means salvation.
In answer to the first part of your question, all you need to do is ask it at any state or federal penitentiary. There are hundreds of people in jail who have repented of what they did wrong, but they have to suffer the consequences anyway. I think particularly of Jeffery Dahmer. Dahmer is one of the most notorious mass murderers, and even ate his victims. While in prison he came to faith in Jesus and was baptized for forgiveness of his sins, yet he not only stayed in prison but insisted that he should pay the penalty on earth for his sins. Although his decisions resulted in his physical death, he knew that the physical punishment on earth was only for a short time, but that he would not suffer eternal punishment.
It is a rule with God that sin results in punishment. "If I sin, then thou markest me, and thou wilt not acquit me from mine iniquity." (Job 10:14) "The soul that sinneth, it shall die." (Ezekiel 18:4) God does tell Ezekiel that those who change their ways and follow him will be forgiven. But that still does not do away with punishment.
That is where Jesus comes in. God requires punishment for sin. Jesus took that punishment upon himself. "So Christ was once offered to bear the sins of many." (Hebrews 9:28) If we accept the sacrifice of Christ through faith, repentance, and baptism, then we need not be punished by God for our sins. Jesus took the punishment in our place.
The last part of you question asks if we can repent and still not be saved, or if repentance is possible at all without salvation. Obviously even the ones who are not saved can repent. The jails are full of people who are sorry for their crimes and promise not to do them again. There are a lot of such people outside the jails, too. But many are not willing to put their faith in Jesus and accept his offer of salvation. They repent, but not enough to be saved. "For godly sorrow worketh repentance to salvation not to be repented of: but the sorrow of the world worketh death." (2 Corinthians 7:10) Paul says there is a sorrow or repentance of the world, but it works death, not salvation. So it is possible to repent and yet not be saved. Godly repentance causes one to obey God in all things, as is needful for salvation.