A list of differences between USCF and FIDE rules: http://www.uschess.org/images/stories/FIDEInformation/uschess-fide-rules-twocolumn-comparison-feb2020-rev-2.pdf
Some highlights: Can an arbiter call a flag, can you call your own flag, can an arbiter call a touch violation without a claim, how complete a score you need to get a flag win, when you can claim ...
Is chess played by exactly the same rules around the whole world?
No. To be honest, as outlined below, even FIDE rated chess is played by slightly different rules because the FIDE Laws give this flexibility
According to the preface of the FIDE Laws of Chess:
A necessary condition for a game to be rated by FIDE is that it shall
be played according to ...
Here's an example of a "possible series of moves" from FIDE rules 9.6, so White can technically (despite nearly impossible in reality) be checkmated:
[FEN "8/4k3/4P3/3B2P1/4P1K1/8/3b4/8 w - - 3 67"]
67. Kh5 Kf8 68. Kh6 Bb4 69. Kh7 Bd6 70. e5 Bxe5 71. Be4 Bd6 72. Kh8 Ba3 73. Bh7 Bb2#
Does this rule stand in major Chess tournaments?
This rule applies in all tournaments where FIDE Laws of Chess take precedence. So, yes, it applies in all major tournaments including USCF and all federations which are affiliated to FIDE.
If it appears to not work on a particular website then that is likely a bug on the platform and it is worth reporting to ...
This is a case that is decided by the director's discretion.
18G. Adjudications. Only under emergency circumstances may a director permanently adjudicate a game; that is, declare a result based upon best play by both sides.
An interesting rule is:
15G. Ownership of scoresheets The scoresheets of all games in a tournament are the property of ...