To start with this is the table of elementary particles:
A corresponding table exists for antiparticles for the blue and the green colored ones, which are fermions. From the rest which are bosons the neutral ones are the antiparticles of themselves, and the antiparticle of W+ is W- and vice verso.
By definition the antiparticle has the opposite in numbers quantum numbers of a particle.
These are the building blocks of matter.
The resonances, the baryons, proton neutron, and the nuclei that are built up by baryons correspondingly have their antiparticles .
(1) aP is made of the "usual" elementary particles, and indeed the same elementary particles as P, but arranged (or something) in some different way,
the antiparticles are made up by the elementary particles in the antiparticle table.
(2) aP is made of the "usual" elementary particles, but it is made of some different set of elementary particles than P,
same answer as 1),
(3) aP is in fact made of not the usual elementary particles, but, is made of anti-elementary particles.
Yes, antiparticles are as valid as particles, except we live in a universe where particles dominate, leading to the baryon asymmetry, the CP violation
In particle physics, CP violation (CP standing for charge parity) is a violation of the postulated CP-symmetry (or charge conjugation parity symmetry): the combination of C-symmetry (charge conjugation symmetry) and P-symmetry (parity symmetry). CP-symmetry states that the laws of physics should be the same if a particle is interchanged with its antiparticle (C symmetry), and when its spatial coordinates are inverted ("mirror" or P symmetry).
It is still an open research problem to explain why our universe is made mainly out of particles, without resorting to the anthropic principle