Organic compounds with antibacterial and antiparasitic properties are gaining significance for biomedical applications. This study focuses on the solvent-free synthesis (green synthesis) of 1,4-naphthoquinone or 2,3-dichloro-1,4-naphthoquinone with different phenylamines using silica gel as an acid solid support. The study also includes in silico PASS predictions and the discovery of antibacterial and antiparasitic properties of phenylaminonaphthoquinone derivatives 1–12, which can be further applied in drug discovery and development. These activities were discussed in terms of molecular descriptors such as hydrophobicity, molar refractivity, and half-wave potentials. The in vitro antimicrobial potential of the synthesized compounds 1–12 was evaluated against a panel of six bacterial strains (three Gram-positive: Staphylococcus aureus, Proteus mirabilis, and Enterococcus faecalis; and three Gram-negative bacteria: Escherichia coli, Salmonella typhimurium, and Klebsiella pneumoniae). Six compounds (1, 3, 5, 7, 10, and 11) showed better activity toward S. aureus with MIC values between 3.2 and 5.7 μg/mL compared to cefazolin (MIC = 4.2 μg/mL) and cefotaxime (MIC = 8.9 μg/mL), two cephalosporin antibiotics. Regarding in vitro antiplasmodial activity, compounds 1 and 3 were the most active against the Plasmodium falciparum strain 3D7 (chloroquine-sensitive), displaying IC50 values of 0.16 and 0.0049 μg/mL, respectively, compared to chloroquine (0.33 μg/mL). In strain FCR-3 (chloroquine-resistant), most of the compounds showed good activity, with compounds 3 (0.12 μg/mL) and 11 (0.55 μg/mL) being particularly noteworthy. Additionally, docking studies were used to better rationalize the action and prediction of the binding modes of these compounds. Finally, absorption, distribution, metabolism, excretion, and toxicity (ADMET) predictions were performed.