If you’re sure it was a hearing aid, it might be a slightly outdated version. The actual hearing aid would be a microphone/remote, probably worn around the neck or in a pocket. The wires most likely have a speaker concealed right behind her ear (in the place where people tuck hair behind their ears, or where the point on an elf’s ear would be). The actual hearing aid (/microphone/remote) can often be used to connect to a transmitter through a wireless signal. The transmitter can be plugged into an iPod, TV, computer, etc.

In answer to your other questions, the effect of wearing a jacket or coat would depend on the strength of the hearing aid. As I said, it is most like worn around the neck, in which case it is hardly affected at all. If several layers of heavy material were over it, or if it was in a pocket, some hearing aids would be muffled or make scuffling noises from rubbing against the material or from being bounced around. Other hearing aids would have no problem at all.
To hear better on the phone, her hearing aid probably has a bluetooth capability. The microphone on the remote would enable her to talk, and the speaker behind the ear would enable her to hear. It would probably sound no different than a regular phone.
This woman is probably hard-of-hearing, not deaf, and would have learned English just like everyone else. Her speech might be a little slurred, and some of the softer sounds (such the s or the f) would be underpronounced.

I hope this helps. Sorry for the long answer, I wanted to make sure I covered everything. If you would like any other questions answered, feel free to message me from my Yahoo Answers page.

Older cochlear implants were connected to their processor by a cord; however, the latest cochlear implants have become much more compact and all parts are worn near the ear.

As mentioned an ALD is something used in conjunction with the hearing aids to allow improved hearing in noisy situations or allow a hearing aid that does not have wireless capabilities to interface with a cell phone or audio device via an induction/telecoil loop.

Body worn hearing aids are no longer sold and I highly doubt anyone is still wearing them. Historically body worn devices were still worn by persons with severe hearing loss but with today digital hearing aids and small electronic parts used to make hearing aids, even the most powerful hearing aids are compact and worn ear level.