You could launch some missiles, blow a few satellites into smithereens, and gradually over the next few months they would take out the others. That's a poor kind of war weapon. An effective weapon is one where you can inflict damage continuously, and are able to stop immediately upon some concession. If you can't offer to stop in return for concessions, you won't get any.

You don't take down satellites in order to force someone to negotiate, you take them down for denial of capabilities.

Its not really that easy, to cause such a chain reaction, specially if the other person reacts.

And its also really expensive, each sat you take down costs you far more then what you hit. So unless you can actually cause a chain reaction its a losing proposition.

Not really. That’s more science fiction than reality. You should try some Kerbal Space Program and explore how orbits are affected by thrust = collisions, in different directions.

As soon as a satellite is hit the rest of the fleet can start thrusting and raise their orbits to create a clear separation to the debris field.

Following such an attack the rest of the fleet would of course spread out across orbital heights and planes to minimize the potential damage done by each hit, leading to maximum cost for the adversary to do any damage. Rather than like today where the orbits are optimized for ease of management and highest possible bandwidth.