what are the differences between thanks and thank?
other than that,
no worries, , why not no worry instead of worries?
same goes, why not same go ?
It depends on the context. For example, we often say "Thanks for that". In this sentence, "thanks" is a plural noun, because the sentence is really a short way of saying "(I give you) thanks for that." But "thank" is also a verb, so we can say "I thank for you for helping me" or "He thanks you for helping him." In the latter sentence, "thanks" is the third-person present form of "to thank". The way to remember it is that "thanks" as a noun is always plural (you cannot give "a thank" - although you can give "a big thank-you"). If it's a verb, it behaves regularly, and it should be obvious whether a noun or verb is meant from the context.
"No worries" (on its own) is an idiom from Australian English ("strine"), which has become more popular now outside Australia. As part of a sentence though, it is just as correct to say, for example, "You'll have no worry about getting your money back" as "You'll have no worries about getting your money back." It's a matter of preference.
"The same" is a thing, so "to go" takes its third-person form "goes".