Recent observations of sunspot's umbra suggested that it may be finely structured at a sub-arcsecond scale representing a mix of hot and cool plasma elements. In this study we will report the first detailed observations of the umbral spikes, which are cool jet-like structures seen in the chromosphere of an umbra. The preliminary analysis indicates that the spikes are not associated with photospheric umbral dots and they rather tend to occur above darkest parts of the umbra, where magnetic fields are strongest. The spikes exhibit up and down oscillatory motions and their spectral evolution suggests that they might be driven by upward propagating shocks generated by photospheric oscillations. We analyze sunspot oscillations using Interface Region Imaging Spectrograph (IRIS) slit-jaw and spectral data and narrow-band chromospheric images from the New Solar Telescope (NST). The intensity of chromospheric shocks displays a long term (about 20~min) variations. Data allowed us to conclude that sunspot umbral flashes (UFs) may appear in the form of narrow bright lanes running along the light bridges and surrounding clusters of umbral bright points. Time series also suggested that UFs preferred to appear on the sunspot-center side of light bridges, which may indicate the existence of a compact sub-photospheric driver of sunspot oscillations. The sunspot's umbra as seen in the IRIS chromospheric and transition region data appears bright above the locations of light bridges and the areas where the dark umbra is dotted with clusters of umbral dots. Co-spatial and co-temporal SDO/AIA data showed that the same locations were associated with bright footpoints of coronal loops suggesting that the light bridges may play an important role in heating the coronal sunspot loops. Finally, the power spectra analysis showed that the intensity of chromospheric and transition region oscillations significantly vary across the umbra and with height, suggesting that umbral non-uniformities and the structure of sunspot magnetic fields may play a role in wave propagation and heating of umbral loops.