Q: file recovery after partition deletion

GPT is the correct choice. You can guess how big the disk image will be but it may not fit on the same disk, hence an external disk is the easier and cleaner option.

If you have an identical disk, as an external and it can used solely for this, there is command called dd (disk dump) which will allow an exact image of the internal disk on an external disk. Such an image is the best method of a storing the data on this disk.

Your internal disk is 320GB from the Testdisk output. Is your Seagate a GUID partition disk with about 400GB free?

If the Seagate is formatted as NTFS (or FAT), you can create an additional FAT partition, roughly 400GB, connect the disk to the Mac and choose this new partition on the external disk as the destination for the DMG (disk image) file.

If you can write a small file to the external Seagate as a test and it succeeds, you can create the DMG directly on the external disk.

No. The destination should be the Seagate for the disk image. The source should be your full disk. You need to select the outermost internal disk in utility, and then click on New Image. Choose options as appropriate and make sure the destination file is on the Seagate disk.

I cannot see your screen shot.

1. Can you check the format of the Seagate disk?

2. If you click on the Hitachi entry, and click on New Image, can you write the image to the Seagate?