A bit of research showed me that a lot of these countries have a Han-Viet name and not everyone is familiar with them. So instead, I present the common, most familiar name for each of the countries.
Please refer back to the post on Addressing People, in order to answer and ask questions correctly.
V = Bạn từ nước nào?
P = B'an' (as in t'an'trum) teu neurk now?
E = Which country are you from?
Reply:
V = Tôi từ...
P = Toy teu...
E = I am from...
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V = Bạn là người nước gì?
P = B'an' lah nguh-ee neurk zee?
E = What is your nationality?
Reply:
V = Tôi là người...(remove the word 'nước')
P = Toy lah nguh-ee...
E = I am...
__________________________________________________________________________
V = Nước Úc
P = Neurk 'Oo'p (as in p'oo'l)
E = Australia
V = Nước Ba Tây
P = Neurk Baah Tey
E = Brazil
V = Ca-na-da / Gia Nả Đại
P = Ga-na-da
E = Canada
V = Nước Trung Quốc
P = Neurk Joom Gwook
E = China

P = Neurk 'Ang' (as in s'ang')
E = England
V = Nước Pháp
P = Neurk Fahp
E = France
V = Nước Đức
P = Neurk Deuk
E = Germany
V = Nước Hồng Kong
P = Nuerk Holm Kolm
E = Hong Kong

P = Neurk Uhn Door
E = India
V = Nước Inđônêsia
P = Neurk In-door-neh-see-ah
E = Indonesia

P = Neurk Eye-lehn
E = Ireland
V = Nước Ý
P = Neurk 'Ea' (as in 'ea'sy)
E = Italy
V = Nước Nhật Bản
P = Neurk Nhuh-t Bahn
E = Japan
V = Nước Hàn Quốc
P = Neurk Hand Gwook
E = Korea

P = Neurk Mah Lie
E = Malaysia
V = Nước Mêhicô
P = Neurk Mê-he-gaw
E = Mexico
V = Nước Niu Di-lân
P = Neurk Nee-ew Zee-l'un' (as in n'un')
E = New Zealand
V = Nước Phi
P = Neurk Fee
E = Philippines
V = Nước Nga
P = Neurk 'Ng'aa (as in si'ng')
E = Russia
V = Nước Tân Gia Ba
P = Neurk Tun Zaa Baa
E = Singapore

P = Neurk Mee
E = USA