I worked for some time repairing hearing aids--they are a nightmare!
The main types I worked on were analog types with digitally programmable characteristics.
These devices could be programmed for the required frequency response,dynamic range,gain etc,as determined by the Audiologist examining the wearer.
They use an "earphone" unit,in the body of the aid,with the sound fed to the earmould via plastic or rubber tubing.
The "in ear" devices used very short lengths of tube,& the "behind the ear" & the (very few) "pocket" units,a short tube between the earphone & an external tube cast into the body,which then had a long tube to the earmould.
The main things that went wrong,were the tubes coming loose in the earmould,(which caused weird echoing sound with the "in ear" units,& loss of sound in the other types),& earwax blocking of the earmould outlet,& in some models,the earphone & microphone .
Sometimes such problems would not be diagnosed & the Audiologist would re-program the aid,so that if you later repaired it,they would need to restore the previous program.
Just before I left,they brought in fully digital aids,which initially were very unpopular among the clients,due to high background noise & reliability problems.
Those problems seem to have been overcome now.
The Telecoils I recall were wound on small "dogbone"ferrites.
I have no idea of their inductance,but I would guess greater than 50uH.