Complex formation between a weak flexible polyelectrolyte chain and one positively charged nanoparticle in presence of explicit counterions and salt particles is investigated using Monte Carlo simulations. The influence of parameters such as the nanoparticle surface charge density, salt valency, and solution property such as the pH on the chain protonation/deprotonation process and monomer adsorption at the nanoparticle surface are systematically investigated. It is shown that the nanoparticle presence significantly modifies chain acid/base and polyelectrolyte conformational properties. The importance of the attractive electrostatic interactions between the chain and the nanoparticle clearly promotes the chain deprotonation leading, at high pH and nanoparticle charge density, to fully wrapped polyelectrolyte at the nanoparticle surface. When the nanoparticle bare charge is overcompensated by the polyelectrolyte charges, counterions and salt particles condense at the surface of the polyelectrolyte-nanoparticle complex to compensate for the excess of charges providing from the adsorbed polyelectrolyte chain. It is also shown that the complex formation is significantly affected by the salt valency. Indeed, with the presence of trivalent salt cations, competition is observed between the nanoparticle and the trivalent cations. As a result, the amount of adsorbed monomers is less important than in the monovalent and divalent case and chain conformations are different due to the collapse of polyelectrolyte segments around trivalent cations out of the nanoparticle adsorption layer.