Not a doctor or any profession of relevance but I do use tanning lights. Incandescents produce mostly visible light and very little UVA or UVB for those health concerns. Fluorescents tend to produce more UVB in comparison but still very negligible. Tanning lights generally produce the amount of UVA and UVB needed for vitamin D synthesis although you have to use with caution.

No, they don't produce any UV light.

Even if the filament somehow does (I doubt it), it won't make it through the glass of the bulb.

I don't think incandescent bulbs produce any significant UV. The temperature is too low.