Cannot Format External HDD Except To ExFat

My 1TB external hard drive worked just fine. I used to store there everything. It was using NTFS file system. Last week I connected it to my laptop and it was really slow when I tried to move or delete files from my pc to the drive. I disconnected and reconnected it to my laptop. Suddenly, it said that I had to format it! I couldn't even access it neither the files in it. I managed to take some of the files to my laptop using recovery software and they are now safe. I thought the trouble would be gone now. I thought now I would just format it and store my files again. I was wrong. I can't even format it!

I tried disk management, cmd, almost everything. I downloaded various programs to run tests and try to write everything zeros. Turned out quitting that cause it tells me it needs a lot of hours. So, I tried a different approach that I was so stupid not to have tried yet. I tried formatting in other file system. I tried and it worked, well, almost... I can only successfully format it to exFat with the 'quick format' option enabled. If that option isn't enabled or I try to format it to NTFS, the formatting process takes forever or crashes. I would stay with my HDD formatted to exFat, but it is too slow..