How do I calculate parameters of LC filter from component values?
Calculating the results you want by hand would result in reams of paper spent on algebraic manipulation. Likely a tool like Maple or Mathematica could do the grunt work for you, but you'd end up with a giant ratio of complex polynomials, likely with about 7 or 8 terms each, which wouldn't lend much to understanding the behavior of the circuit.

Much easier is to simply simulate the circuit in any SPICE-like simulator. You can get the results you want using an AC simulation.

First, realize that "characteristic impedance" is a property of transmission lines, and not a term normally used for filters like this one. You are probably interested in either the input impedance, output impedance or both.

To get the input impedance, in your simulator, apply an AC current source with amplitude 1 to the input, and run an AC simulation over the frequency range you're interested in. The resulting voltage at the input node is numerically equal to the input impedance.

To get the output impedance, just reverse the circuit and do the same simulation with the source connected to the output node.

To get the frequency response, assuming you want a voltage transfer function, apply an AC voltage source at the input and measure (plot) the response at the output. With such a high-order circuit, if it wasn't designed to have one there may be no obvious "corner" frequency, in which case you'll have to define what you want --- maybe you want the point where the voltage response falls by half, or by square-root-of-2.

In all of these simulations, to understand the filter's behavior in your system, you'll want to terminate the output port (or input port for the output impedance measurement) with an appropriate load.

Also, for high order filters like this, the response can be strongly affected by small variations of the component parameters. If you want to know how the real circuit will behave when you build it, be sure to do some tolerance analysis (simulate with different values of the different components, depending on the tolerances you're willing to pay for) before moving on to physical construction.