Model 0.3 wt% and 1 wt% Pd/Beta was synthesized with nano-sized Beta crystals (average size < 50 nm) and defect-free large micrometer sized crystals with similar Si/Al ratios similar to 13 and 15. With the aid of FTIR we reveal the formation of at least two Pd(II)-NO and one Pd(I)-NO complexes upon NO adsorption on those materials under conditions relevant to PNA. Under higher NO pressures at room temperature, we detect the formation of the first palladium(II) dinitrosyl Pd(NO)(2) complex, not observed previously on the solid supports or in organometallic compounds. O-2 in dry streams promotes NO storage via additional formation of nitrosyl (NO+) ions; it also leads to stabilization of significant amounts of N2O3 in BEA pores. In the presence of water, NO storage capacity is dramatically lowered. However, in the presence of CO (which is always present in exhaust gas) the performance improves. With the aid of spectroscopy and PNA measurements we show that in the presence of CO, stable mixed palladium(II) carbonyl nitrosyl complex [Pd(II)(CO)(NO)] is formed and responsible for enhanced NOx storage. This points to a general conclusion that the species responsible for NOx storage on various zeolites in the presence of water and CO, are in fact, Pd(II)(CO)(NO). Decreasing the Pd loading to 0.3 wt% improves Pd dispersion and NO/Pd storage ratio. We also demonstrate that varying crystal sizes of BEA leads to significant changes in the NOx release temperature as well as NO/Pd ratio. Larger, defect free, more hydrophobic BEA crystals store more NOx and release it at higher temperature. Furthermore, larger, defect free and more hydrophobic BEA crystals stay significantly more active for PNA after hydrothermal aging, losing little activity compared with defective nanocrystals. High-field Al-27 NMR results show that larger, hydrophobic BEA crystals are more resistant to de-alumination upon hydrothermal aging (HTA), and thus are more attractive for PNA storage with Pd.