Re: What is the difference between "think right" and "right think"?
I think you have heard someone speaking what I suppose is charitably called a dialect that is found in a few areas of Britain. In the words you quote, the 'g' in 'thing' is pronounced as a 'k'. So:
'It's the right thing to do' is spoken as 'It's the right think to do'
'He can't do a damn thing right' is spoken as 'He can't do a damn think right'
Other changes in spoken speech are:
mother : muvva
brother : bruvva
with : wiv
breathe : breeve
breath : breff
't' and 'tt' is replaced in certain words with a glottal stop:
bottle : bo-ul
isn't it :init
(I wince and grimace when I hear people talking like this.)