Maybe pondering on permeability values of different matters could give some approach to your questions?
An air core coil 'sees' matter inside and outside with a permeability of 1, hence flux has no reson to attract or repel to anything. Here you may consider using iron wire instead of copper: then the very vicinity of the air coil includes a ferromagnetic material with permeability much higher than air, flux will be very much confined with respect to copper wire air core coil, no?
And then you put low permeability powder iron into the air core coil, you get again a flux-collected situation because most of the flux would prefer to 'propagate' inside the soft iron core and much less flux will be 'strayed' if you compare this to air core coil.
Now all this influences the quality factor, Q of the air core coil, meaning here the use of silver coated wire: the goal is to reduce losses. (Notice that the more flux goes outside of the air core coil i.e. gets strayed', the less Q you get, if you lose flux you get more loss.)
On the other hand, air cored transformers do exist and used anywhere from some MHz frequencies up to microwaves, mainly for power transfer, and in these cases resonance for such coils are often utilized too (I am not an expert on these, sorry). A google search with HF air core transformer brings many hits.
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