The magnetic properties and pseudocritical behavior of ferromagnetic pure and metallic nanoparticles having concurrently atomic disorder, dilution, and competing interactions, are studied in the framework of an Ising model. We have used the free-energy variational principle based on the Bogoliubov inequality and Monte Carlo simulation. As a case of study for random diluted nanoparticles we have considered the Fe${}_{0.5}$Mn${}_{0.1}$Al${}_{0.4}$ alloy. It is characterized for exhibiting, under bulk conditions, low-temperature reentrant spin-glass (RSG) behavior. Besides, experimental and simulation results are available for that alloy. Our results allow to conclude that the variational model is successful in reproducing features of the particle size dependence of the ordering temperature for pure and random diluted particles. In this last case, low-temperature magnetization reduction was consistent with the same type of RSG behavior observed in bulk in accordance with the Almeida-Thouless line at low fields. A linear dependence of the freezing temperature with the reciprocal of the particle diameter was also obtained. Computation of the correlation length shift exponent for random diluted nanoparticles yielded the values $\ensuremath{\nu}=0.926\ifmmode\pm\else\textpm\fi{}0.004$ via Bogoliubov simulations and $\ensuremath{\nu}=0.71\ifmmode\pm\else\textpm\fi{}0.04$ via Monte Carlo simulations. Differences are attributed to the spin pair approximation used in the variational model. From both approaches, differences in the $\ensuremath{\nu}$ exponent of Fe${}_{0.5}$Mn${}_{0.1}$Al${}_{0.4}$ nanoparticles with respect to that of the pure Ising model agree with Harris and Fisher arguments.