Learn English – What does “Take care sweets” mean

Even I've tried to find references and failed. I can share my personal experience here, though, assuming the OP is a fellow Indian.

"Country fellow" is a slightly offensive phrase in south India. It is merely a direct translation of the words from south Indian languages (Malayalam, Tamil, etc.), for example, "naadan chekkan" in Malayalam.

It has nothing to do with the original meaning of fellow countrymen. What it actually means is a person who is cultureless; or someone not trendy enough (among a group of friends, mostly).

Suppose three friends are discussing western music (say, a rap song by Eminem). If one of them tells that he likes Indian carnatic music more, then the other two might say "Oh, grow up! Don't be such a country fellow".

I hope my explanation is clear. I couldn't find any reliable reference to add here. Perhaps it's enough that searching "country fellows" on google will have results related to south Indian slang.

It can also mean "people from the countryside", but that doesn't usually apply when used among friends.

Dictionary.com has a definition for clunk as follows:

4. Informal. a stupid person; clunkhead.

However, as FumbleFingers remarks in a comment to the question, it is a rare epithet. Searching for "we were clunks", the mighty engine can tell me in 0.17 seconds that the result is unique in cyberspace. Out of the 46 results given for "we were both clunks", 44 of them are direct quotations of that book, and the first and second results link to this question.