1. As mentioned before, legibility is key. Publishers might have their own house formatting rules, but there isnt anything wrong with p,i,m,a
on the same side of the staff / notes.
2. Partial barre is usually 1/2, or a C with a slash through it, despite the number of strings barred. The context of the piece and the player's hand determine whether a partial or full barre is used.
Some publishers use other notes, such as this: 3/3, which means start on string 3 and cover 3 strings with the barre. A bit of overkill if you ask me, because there is no other way to play the chord, but its their choice.
I don't know of any specific notation for the hinge, usually if a hinge barre is needed it will be because there is an open string somewhere, which you would indicate by using "0" as the left hand fingering for that note. You could write the word "hinge" but if you are careful with the rhythmic notation and RH fingering, the hinge will be implied anyway.
3. Rasgueado and/or strums can be notated several different ways, some more precise than others.
Sometimes, direction and fingering, and even number of "strums" or fingers needed aren't specified. (last few measures of this example just use a plain "arpeggiate" sign...the squiggly line, and don't specify one finger or several fingers) :
Sometimes, direction is specified.
Sometimes, direction and finger are both specified:
(i used this example earlier)
In any case, if you have a reason for very specific fingerings and notations, you might want to include a glossary at the beginning of the piece.
I know you didn't ask about this so forgive my intrusion, but fingerings are often left to the performer...otherwise the score gets overcluttered.
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2015 John H. Dick
1994 Larry Breslin ("Deerhead")
1952 Vincente Tatay