How to get my files of a Windows-formatted HDD?
All newer Mac OS X systems are capable of reading all common Windows file systems (FAT/FAT32/NTFS) right out of the box. So it shouldn't be a problem to access the contents of the internal HDD connected to your drive dock, given that the Unitek is working with your Mac.  

Since you didn't use any special backup software (generating unaccessible file formats) the same should be valid for your external HDD.