1) You choose a suitable impedance that the transmitter can drive. The transmitter's current output must be able to get enough voltage across the receiver to meet the link specification for signal levels.
Almost always this is 100ohm balanced, or two complemently 50ohm lines. This is usually specified by the supplier or the SERDES chips. It is this impedance because a) it is 'about right' for sensible voltage and current levels on the interface b) it matches standard test gear connections c) it uses 'reasonable' dimensions on a PCB.
Knowing the impedance, you then choose line dimensions (width, spacing, thickness) for the PCB that will present that impedance. All good PCB manufacturers will be able to tell you dimensions for their process that will end up giving you the right impedance.
You then look at the SERDES specification and see whether the receiver already has line termination in it, or whether you have to implement that externally, and leave the end of the line open or connected to a resistor as required.
2) The impedance of a trace does not depend on the its length.
3) As explained in (1), traces must be deisgned to present the right impedance. Depending on whether the line is single or double-ended, source or destination or doubly terminated, resistors must be used for termination, and must have a value matching the trace.
Generally for point to point SERDES, the line is simply connected between the transmitter and the receiver, with the manufacturer of the chips having designed the TX output to drive the line directly, and put a suitable termination inside the receiver.