All of this information is readily available, but I’ll fill you in.
The version of Black Mesa you download from the links on the official site’s download page (the one you linked, and the one this forum is on) should be the complete, functional game. There are no official patches that I know of.
The 2 mods you linked to are both fan-made, however, their quality is excellent, and many people play the Black Mesa mod with those two expansions installed. I know I do, and I personally suggest them highly. They fit in seamlessly, and I can’t imagine playing without them.
One thing that’s of note, however, is that On a Rail Uncut is in Beta. So it’s not perfect, however, it’s certainly already quite polished, and perfectly playable. So it’s still worth adding, even though it’s not completely touched-up, in my personal opinion.
Xen is not currently in the game. That portion of the mod is still in development. The Current version of the game that has been released ends after Lambda Core.