The optical properties and functionality of air-stable PbSe/PbS core-shell and PbSe/PbSexS1-x core-alloyed shell nanocrystal quantum dots (NQDs) are presented. These NQDs showed chemical robustness over months and years and band-gap tunability in the near infrared spectral regime, with a reliance on the NQD size and composition. Furthermore, these NQDs exhibit high emission quantum efficiencies of up to 65% and an exciton emission band that is narrower than that of the corresponding PbSe NQDs. In addition, the emission bands showed a peculiar energy shift with respect to the relevant absorption band, changing from a Stokes shift to an anti-Stokes shift, with an increase of the NQD diameter. The described core-shell structures and the corresponding PbSe core NQDs were used as passive Q-switches in eye-safe lasers of Er:glass, where they act as saturable absorbers. The absorber saturation investigations revealed a relatively large ground-state cross-section of absorption (sigma(gs)=10(-16)-10(-15) cm(2)) and a behavior of a "fast" absorber with an effective lifetime of tau(eff)approximate to 4.0 ps is proposed. This lifetime is associated with the formation of multiple excitons at the measured pumping power. The product of sigma(gs) and tau(eff) enables sufficient Q-switching performance and tunability in the near infrared spectral regime. The amplified spontaneous emission properties of PbSe NQDs were examined under continuous illumination by a diode laser at room temperature, suitable for standard device conditions. The results revealed a relatively large gain parameter (g=2.63-6.67 cm(-1)). The conductivity properties of PbSe NQD self-assembled solids, annealed at 200 degrees C, showed an Ohmic behavior at the measured voltages (up to 30 V), which is governed by a variable-range-hopping charge transport mechanism.