"The famous Russian writer is sitting and writing by the tree."
Translation:A híres orosz író a fánál ül és ír.
Usually if we have more than one predicate with the same adjunct we tend to put the adjunct first. I'm not sure if it's an actual rule or just a collective habit but I doubt any native speaker would use your version.
Actually, word order is important. It is a very powerful tool in the Hungarian language, letting us express so many things with the same few words.
But it is flexible, for sure. :)
That Hungarian has free word order, must be the most misleading claim about this language.
If I may try to fix it: What is true is that the grammatical role of a word is not determined by its position in the sentence but rather its endings.
Very unlike English, which has trashed almost all grammar inflection in favor of grammar based on strict word order.
Thus, in some ways, the word order in Hungarian contributes more to meaning than in English.