We considered Weinberg-like equations in the article [1] in order to construct the Feynman-Dyson propagator for the spin-1 particles. An analog of the $S=1/2$ Feynman-Dyson propagator is presented in the framework of the $S=1$ Weinberg's theory. The basis for This construction is based on the concept of the Weinberg field as a system of four field functions differing by parity and by dual transformations. Next, We also analyzed the recent controversy in the definitions of the Feynman-Dyson propagator for the field operator containing the $S=1/2$ self/anti-self charge conjugate states in the papers by D. Ahluwalia et al~cite{Ahlu-PR} and by W. Rodrigues Jr. et al~cite{Rodrigues-PR,Rodrigues-IJTP}. The solution to this mathematical controversy is obvious. I proposed the necessary doubling of the Fock Space (as in the Barut and Ziino works), thus extending the corresponding Clifford Algebra. However, the logical interrelations of different mathematical foundations with physical interpretations are not so obvious. In this work we present some insights with respect to this for spin 1/2 and 1. Meanwhile, the N. Debergh et al article considered our old ideas of doubling the Dirac equation, and other forms of T- and PT-conjugation [5]. Both algebraic equation $Det (hat p - m) =0$ and $Det (hat p + m) =0$ for $u-$ and $v-$ 4-spinors have solutions with $p_0= pm E_p =pm sqrt{{bf p}^2 +m^2}$. The same is true for higher-spin equations (or they may even have more complicated dispersion relations). Meanwhile, every book considers the equality $p_0=E_p$ for both $u-$ and $v-$ spinors of the $(1/2,0)oplus (0,1/2))$ representation only, thus applying the Dirac-Feynman-Stueckelberg procedure for elimination of negative-energy solutions. The recent Ziino works (and, independently, the articles of several other authors) show that The Fock space can be doubled on the quantum-field (QFT) level. We re-consider this possibility on the quantum-field level. In this article we give additional bases for the development of the correct theory of higher spin particles in QFT. It seems, that it is imposible to consider the relativistic quantum mechanics appropriately without negative energies, tachyons and appropriate forms of the discrete symmetries, and their actions on the corresponding physical states.