I made upgrade for Parallels desktop, but need to run it an activation code. Do I have to pay for it again?
No, you should have your serial number for PD still. If not and you bought it from them you can go to your account settings on their homepage after logging in as you and get your serial again.
In account settings I have activation code for PD 6. I dont have the activation code to upgrade to PD 7 or 8.
You may want to get a hold of customer support there. Skipping versions sometimes requires a little more help.