We investigated the hysteresis, pseudo-critical, and compensation behaviors of a quasi-spherical FeCo alloy nanoparticle (2 nm in diameter) using Monte Carlo simulations with thermal bath-type algorithms and a 3D mixed Ising model. The nanostructure was modeled in a body-centered cubic lattice (BCC) through the following configurations: spin S=3/2 for Co and Q=2 for Fe. These simulations reveal that, under the influence of crystal and magnetic fields, the nanoparticle exhibits compensation phenomena, exchange bias, and pseudo-critical temperatures. Knowledge of this type of phenomena is crucial for the design of new materials, since compensation temperatures and exchange bias improve the efficiency of advanced magnetic devices, such as sensors and magnetic memories. Meanwhile, pseudo-critical temperatures allow the creation of materials with controlled phase transitions, which is vital for developing technologies with specific magnetic and thermal properties. An increase in single-ion anisotropies within the nanosystem leads to higher pseudo-critical and compensation temperatures, as well as superparamagnetic behavior at low temperatures.