  The number of extrasolar planets discovered is increasing, so that more than
five thousand exoplanets have been confirmed to date. Now we have an
opportunity to test the validity of the laws governing planetary systems and
take steps to discover the relationships between the physical parameters of
planets and stars. Firstly, we present the results of a search for additional
exoplanets in 229 multi-planetary systems that house at least three or more
confirmed planets, employing a logarithmic spacing between planets in our Solar
System known as the Titius-Bode (TB) relation. We find that the planets in
$\sim53\%$ of these systems adhere to a logarithmic spacing relation remarkably
better than the Solar System planets. We predict the presence of 426 additional
exoplanets, 47 of which are located within the habitable zone (HZ), and five of
the 47 planets have a maximum mass limit of 0.1-2$M_{\oplus}$ and a maximum
radius lower than 1.25$R_{\oplus}$. Secondly, we employ efficient machine
learning approaches to analyze a dataset comprising 762 confirmed exoplanets
and eight Solar System planets, aiming to characterize their fundamental
quantities. We classify the data into two main classes: 'small' and 'giant'
planets, with cut-off values at $R_{p}=8.13R_{\oplus}$ and
$M_{p}=52.48M_{\oplus}$. Giant planets have lower densities, suggesting higher
H-He mass fractions, while small planets are denser, composed mainly of heavier
elements. We highlight that planetary mass, orbital period, and stellar mass
play crucial roles in predicting exoplanet radius. Notably, our study reveals a
noteworthy result: for giant planets, we observe a strong correlation between
planetary radius and the mass of their host stars, which might provide
intriguing insights into the relationship between giant planet formation and
stellar characteristics.
