Core-collapse supernovae (CCSNe) may contribute a significant amount of dust in the early universe. Freshly formed coolant molecules (e.g., CO) and warm dust can be found in CCSNe as early as ~100 d after the explosion, allowing the study of their evolution with time series observations. In the Type II SN 2023ixf, we aim to investigate the temporal evolution of the temperature, velocity, and mass of CO and compare them with other CCSNe, exploring their implications for the dust formation in CCSNe. From observations of velocity profiles of lines of other species (e.g., H and He), we also aim to characterize and understand the interaction of the SN ejecta with preexisting circumstellar material (CSM). We present a time series of 16 near-infrared spectra of SN 2023ixf from 9 to 307 d, taken with multiple instruments: Gemini/GNIRS, Keck/NIRES, IRTF/SpeX, and MMT/MMIRS. The early (t<70 d) spectra indicate interaction between the expanding ejecta and nearby CSM. At t<20 d, intermediate-width line profiles corresponding to the ejecta-wind interaction are superposed on evolving broad P Cygni profiles. We find intermediate-width and narrow lines in the spectra until t<70 d, which suggest continued CSM interaction. We also observe and discuss high-velocity absorption features in H $\alpha$ and H $\beta$ line profiles formed by CSM interaction. The spectra contain CO first overtone emission between 199 and 307 d after the explosion. We model the CO emission and find the CO to have a higher velocity (3000-3500 km/s) than that in Type II-pec SN 1987A (1800-2000 km/s) during similar phases (t=199-307 d) and a comparable CO temperature to SN 1987A. A flattened continuum at wavelengths greater than 1.5 $\mu$m accompanies the CO emission, suggesting that the warm dust is likely formed in the ejecta. The warm dust masses are estimated to be on the order of ~10${}^{-5}{M}_{\odot }$.}