What is your stackup? Where are you routing power and ground? What kind of interfaces are you routing? How fast? These are just some of the questions that would better inform answers to your questions.
Question #1: How to determine the required spacing between length-matched signals or differential pairs and the adjacent layers?
If you are length matching that implies that the interface is probably fast enough to require controlled impedance. So, the trace width and distance to adjacent reference plane is determined by the desired trace impedance.
Trace Impedance Calculator
Also take not of how close your signal layers are to other signal layers. Ideally for a 4-layer stackup, you want your signals close to your reference layers and far away from any other signal layers.
Question #2: How to determine the required spacing between length-matched signals or differential pairs and polygons/copper on the same layer
This one is more of a manufacturing constraint. Your PCB manufacturer will tell you what the track-to-polygon clearance is for their fabrication process. As for signal-to-signal clearance, the PCB manufacturer will give you a number here as well. However, placing tracks as close together as possible may contribute to crosstalk issues which is why it is better to keep tracks away from eachother wherever possible.