"Writing with accent, what is it about?

Writing under influence of mother-language like structures? (I don't mean grammar but words or sentences that tends to be used in a given situation) "

Yeah, that's pretty much what I meant by "writing with an accent". It's the words and sentence patterns we (near-semi-native speakers) use, which are influenced by our mother-language structures, that give us away as being non-native speakers. Nonetheless, our grammar  is usually better than that of average native speakers.