  Contamination due to foregrounds (Galactic and Extra-galactic), calibration
errors and ionospheric effects pose major challenges in detection of the cosmic
21 cm signal in various Epoch of Reionization (EoR) experiments. We present the
results of a pilot study of a field centered on 3C196 using LOFAR Low Band
(56-70 MHz) observations, where we quantify various wide field and calibration
effects such as gain errors, polarized foregrounds, and ionospheric effects. We
observe a `pitchfork' structure in the 2D power spectrum of the polarized
intensity in delay-baseline space, which leaks into the modes beyond the
instrumental horizon (EoR/CD window). We show that this structure largely
arises due to strong instrumental polarization leakage ($\sim30\%$) towards
{Cas\,A} ($\sim21$ kJy at 81 MHz, brightest source in northern sky), which is
far away from primary field of view. We measure an extremely small ionospheric
diffractive scale ($r_{\text{diff}} \approx 430$ m at 60 MHz) towards {Cas\,A}
resembling pure Kolmogorov turbulence compared to $r_{\text{diff}} \sim3 - 20$
km towards zenith at 150 MHz for typical ionospheric conditions. This is one of
the smallest diffractive scales ever measured at these frequencies. Our work
provides insights in understanding the nature of aforementioned effects and
mitigating them in future Cosmic Dawn observations (e.g. with SKA-low and HERA)
in the same frequency window.
