What are some homeopathic solutions to extreme hair loss from thyroid issues?

Individualized. You could read about homeopathic remedies such as nat-mur., graph, sil, thuja, etc. Here: http://www.Vithoulkas.Com/en/books-study/online-materia-medica.Html. However, good homeopathic treatment for this condition will require treatment by a trained homeopathic practitioner. A practitioner directory is here: http://homeopathic.Org/resources/practitioners.
Not proven effective. Truly homeopathic "medications" are made by repeated dilutions, so that the ingredient is not really in the medication anymore (just the "essence" of it remains). That means there is no active ingredient left to cause any benefit. However, that also implies that the homeopathic "medicine" should be pretty harmless, unless some other non-homeopathic ingredients were added.