Detailed study of ELAIS N1 field with the uGMRT -- II. Source Properties and Spectral Variation Of Foreground Power Spectrum from 300-500 MHz Observations

Understanding the low-frequency radio sky in depth is necessary to subtract foregrounds in order to detect the redshifted 21 cm signal of neutral hydrogen from the Cosmic Dawn, Epoch of Reionization (EoR) and post-reionization era. In this second paper of the series, we present the upgraded Giant Metrewave Radio Telescope (uGMRT) observation of the ELAIS N1 field made at 300-500 MHz. The image covers an area of $sim 1.8$ $mathrm{deg}^{2}$ and has a central background rms noise of $sim$ 15 $mu mathrm{Jy}$ $mathrm{beam}^{-1}$. We present a radio source catalog containing 2528 sources (with flux densities > 100 $mu$Jy) and normalized source counts derived from that. The detailed comparison of detected sources with previous radio observations is shown. We discuss flux scale accuracy, positional offsets, spectral index distribution and correction factors in source counts. The normalized source counts are in agreement with previous observations of the same field, as well as model source counts from the Square Kilometre Array Design Study (SKADS) simulation. It shows a flattening below $sim$1 mJy which corresponds to rise in population of star forming galaxies and radio-quiet AGN. For the first time, we estimated the spectral characteristics of the angular power spectrum or Multi-Frequency Angular Power Spectrum (MFAPS) of diffuse Galactic synchrotron emission (DGSE) over the wide frequency bandwidth of $300-500$~MHz from radio interferometric observations. This work demonstrates the improved capabilities of the uGMRT.