1st paragraph: yes; 2nd par.: yes, roughly since 1475 our today's rules and laws; 3rd par.: no, nobody plays by the "old" rules and laws, and yes, there are "old" games recorded, give me some time to search for them !
In my opinion not that "interesting" to see those games, and you cannot compare with modern ones.
Apart from rules and laws, they once played with handicaps, as material odds, e.g. pawn and move or even pawn and two moves, to compensate for the difference in skill between the two players. All this changes the nature of the game and is not done anymore.
I've heard once that earlier chess rules were that the queen moved just one square, like the king, and that there was no en-passant/pawns walking two squares in the first move.
But all the oldest games I've seen, from the "romantic times" of chess and all that, with more crazy Tal-style tactic sequences and insane sacrifices, have already the "new" rules.
Are there sites where you play by the old rules? Are there interesting games recorded from that time, hopefully with someone commenting on youtube or sites like this?
I think it would be quite interesting to see games with those rules, combined with modern knowledge/theory.