No one seems to have touched on the original question. Many languages are free word order, unlike English (and, I think Chinese) which has relatively rigid word order. The ree word order languages all seem to classify nouns into a number of “kinds”, called genders, even though they have no necessary connection to sex and what this usually allows is that the gender and case of words can be used to disambiguate the sentence. So the subject needn’t come first; it is just the noun in the nominative case. And adjectives don’t have to precede (or follow) the noun they modify, since they agree in gender, number, and case, and, unless there are two nouns in the same gender, number, and case there can be no confusion. Actually, the original Indo-European had three numbers, singular, dual, and plural. The reason that the word for “we” in German is “wir”, but in certain German dialects is “mir” is that one of them was dual and the other plural (I forget which was which). There was no necessary connection between gender and sex. There are several words in German for women and girls (die Frau, der Weib, das Maedchen) and they have different genders.
IE was presumably very free word order. Latin was too, but less so. For one thing, some of the forms started to coincide. I think nominative and accusative case were often identical and that is true in German today. But German is not that free word order even though it has gender, number, and case (and, in addition, adjectives are declined for definiteness), so I presume that all this classification is left over. Still you can begin a sentence with anything including the object, just so the next item is the verb. Nonetheless, it would seem that much of this is vestigial and will eventually go the way of the wings on a dodo. I understand that the Baltic languages (Latvian, Lithuanian) still have the original 7 IE cases (nom, gen, dat, acc, abl. loc, voc) and presumably a full suite of inflections. I would assume they still have free word order, but I don’t know this.
I once questioned a Chinese student closely about his native language. One thing he mentioned was that you cannot tell the sex of a Chinese from his/her name. But I asked him how you would say “I will come tomorrow” and he answered that you would say the Chinese equivalent of “I come tomorrow”. I asked him a couple more like that and finally asked about “I will come sometime in the indefinite future” and he replied “I come sometime in the indefinite future”. The point is that they can express as much as they want–or as little. We have no good way of saying “his/her” as I did above except with in the idiotic way I did. In Chinese you don’t have to specify sex, although I am sure you can if you want to. Highly inflected languages force you to be more specific.