Is there evidence for cross-cultural differences in problem solving skills? Does the thought process in our mind for solving a problem or bringing out a solution to a problem depend on culture or language?

If so, how can these skills be represented and addressed?
A bit of a broad question as a full answer will really depend on the specifics of the problem being addressed.

In short though, yes, cultural factors, and probably to some extent linguistic factors as well, do impact on problem solving processes. 

One of the main cross-cultural factors that can alter problem solving is the whole individualism/collectivism distinctions between broader cultural systems and they promote the use of analytic vs holistic perceptual styles. The answer in this post perhaps answers the question in a slightly more applied manner. Another thing to consider can be how certain cultural norms can promote logical vs intuitive reasoning processes as well (see Buchtel &amp; Norenzayan, 2005).

As for language, the general consensus is that it is not the language in and of itself that shapes cognition, but rather the cultural norms or ways of being associated with any given language as a means of cultural communication (See Earle, 1969 for an example).