No.2.
I go for No.2 because No.1, in some places, is not clear which notes actually are muted.
But then, I can’t read music.
Number 2 all the way.
Or any articulation with some words to explain the situation. (for example, all staccatos palm muted)
2, hands down (pun intended)
Agreed. What else would it be? I don’t think it aimed at representing palm mutes in the first place…
Then I misunderstood the OP. I was under the impression they were showing two ways to write palm mute.
Definitely the second one although there’s no reason you can’t emphasize the articulation by writing “palm mutes” without the parenthesis under the notes in question 
That’s how I understood it, too. But then of course the second variation isn’t correct, because as you wrote, the diamond heads indicate harmonics, not palm mute (at least to my knowledge, maybe there are other interpretations).
This is correct, conventional and proper, although you can see that each measure will take much more space horizontally, so that all the brackets fit and clearly define the duration of the P.M. This is something to be considered, depending on the rest of the music on the part.
Personally I find alternate noteheads or any articulation (explained to be the requested technique) easier to read, especially if there are constant changes every second note.
The same goes for dynamics. I’d hate to read a part that has a constant stream of mf, pp, mf, pp, mf, pp, mf, pp under full measures of 16th notes. Just make the pp notes cue-size and explain it at the beginning of the passage.
I would also be perfectly ok with @Rene_L 's traditional undefined-pitch mutes, but notated on their actual pitches, and a x=palm mute legend underneath.
This is the correct way to notate palm mutes. In every guitar book or magazine since the 80s it´s done like this.
I as a guitar player would like to see it exactly like this, simply because I´m used to it.
If the P.M.´s were a little smaller, horizontal space would be less of a problem.
Diamond head notes as already mentioned indicate harmonics.
And “x” is used for a dead note, mostly done by a left hand mute, so this is no approbriate replacement for a palm mute.