Yes, space looks crowded in these visualizations. But the size of the satellites is exaggerated here by thousands of times. Space is huge and the collision risk is extremely low. If displayed at their true size the satellites would not be visible, and indeed the vast majority are not visible in the real life night sky. The exception is recently launched satellites that are still in transit to their final orbits, but even those are only visible sometimes and generally only within an hour or two after sunset or before sunrise.
No, Kessler Syndrome is not a realistic concern for satellites in these orbits. Satellites here experience atmospheric drag and fall out of orbit in five years or so. Collision debris has a higher surface area to mass ratio due to the square-cube law and deorbits faster than that. And it takes a lot less than five years for debris to fall below the orbits of other satellites where it no longer poses any threat of a chain reaction. And no, a collision between two satellites in circular orbits cannot throw debris into much longer-lasting orbits, due to how orbital mechanics works. And even if Kessler Syndrome did somehow happen despite all that, it wouldn't trap us on Earth even for the five year period; a debris cloud would still be quite sparse and launching rockets through it would be no problem since the time spent in the cloud and thus probability of collision would be negligible.