Well, there should be little to no German influence (including Dutch influence, as that was Low German).
For 'great' I assume the word would derive from Vulgar Latin 'grande', Old Norse 'stor', or Anglo-Saxon 'great'.
For 'city', the word would probably derive from 'civitas'. Possibly 'byr'/'borg' from Old Norse or 'burgh' from Old English.
For 'state', the word would almost certainly derive from Latin or Old Norse. So from 'status or 'riki'.
For 'country', the same donor languages. Probably derived from 'pagensis' or 'land'. However, the word 'homeland' might come from Arabic or Gothic.