It sounds like your boyfriend has a pretty serious case of skin and nail fungal infection, which is unfortunately pretty common in diabetics. If he has not seen his primary care doctor
or his diabetes doctor
about this issue, he should do so as soon as possible. Fungal infections in diabetics, especially on the feet, can lead to serious issues, such as chronic foot ulcers, and need to be treated right away.
His doctor will be able to take a look at the extend of the fungal infection and recommend the appropriate treatment. Some of the scaling areas on his hands and feet can probably be treated just fine with a topical anti fungal cream or ointment. However, nail fungus is more difficult to treat, as the topical medications do not penetrate the nails very well. Most cases of nail fungus require extended treatment with oral anti fungal medications.
In terms of your personal concern about contracting skin or nail fungus inside the vagina, this turns out not to be possible. The type of fungus that lives on the skin requires keratin to grow, and keratin is not found in the cells that line the vagina.
I do recommend that you speak with your primary care doctor about general health questions like this, and other considerations you might have about your sexual partner. And please encourage your boyfriend to go see his doctor as well!