It keeps telling me that it was wrongly removed last time, but I have not touch it.
First, how do you have that external Seagate Drive connected to the iMac, ie, via which port?
Secondly, how old is that external drive?
Third, in your first post, you state "I keep getting a message saying that my backup disk (external seagate disk) id taken out wrong", but up above, you stated "It keeps telling me that it was wrongly removed last time, but I have not touch it.". So, does that mean you have not disconnected the external Seagate drive at all?
Fourth, with the drive connected, can Disk Utility "see it"? If it can, run First Aid on that drive and see what it tells you.
Fifth, when you say "I have recently formatted the disk again", how exactly did you do that?
Lastly, do you happen to have a more robust disk maintenance/repair program, like TechTool Pro or Disk Warrior? If not, do you have a friend who has a Mac and has either (or both) of those?