So... we are right back to where we started. The Ubiquity installer is not seeing your HDD or any partitions.
The traceback shows this, as well. First file could not activate new on partition, second could not locate target partition and third, no partition to create.
In your screenshots, it shows you on /dev/sda
You may ask, "But it works on Windows." Windows uses the first available slot, no matter the size, to write and it will fragment however much is needed just to be able to write. Because of this, you can be using Windows on a HDD completely unaware of the fault up to the very moment it finally gives out completely with no apparent warning. Leaves you saying, "Nooo... but... but... my data..."
I would encourage you to boot into Windows and use the Windows Partition Manager to isolate and create a Partition just for Zorin. Format it to ext4, not to NTFS. Then boot your USB and see if you can see that parition and hopefully, it was made where there are good blocks.
Otherwise, again, my own sad opinion is that the HDD is on its last legs and ready to give out.