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In basic terms, using an Ultimate3S Beacon (above) as an example, what do the various toroidal components do exactly? How do they accomplish this?
In construction terms, does it matter if the wound wires touch or overlap? Or does only the number of 'wraps' matter?
Inductors act analogously to a flywheel for electrical current. That is, they want to keep the current steady. To increase or decrease the current requires work, like speeding or slowing a flywheel requires work.
They are the electrical dual of capacitors: capacitors do for voltage what inductors do for current.
In RF applications, inductors (like capacitors) are frequently used as components in filters which accept or reject signals by frequency. They are also used in constructing oscillators, which electrically are really just specialized filters.
Transformers are effectively two or more inductors that share the same core. As the name suggests, they can be used to "transform" impedances by some ratio, analogously to how a gearbox transforms mechanical impedances. This has application in impedance matching. Since the two halves of the transformer aren't connected by any wire, transformers also provide galvanic isolation.
A nice property of toroidal inductors and transformers, versus other shapes, is that the magnetic field lines are almost entirely contained within the toroid. This means they less susceptible to perturbations from other nearby components, and generate less such perturbations themselves. The downside is they are more expensive, since it takes a complicated machine to wind them. If they are being wound by hand this is much less of a concern, which is why toroidal inductors are popular in kits.
The manner in which the wires go through the toroid does not matter too much. It's fine if the wires touch: although the wire may look bare, it's actually coated in an insulating enamel. However, it is best to keep the turns as uniformly spaced and snug as possible.
