The Neem is a large tropical tree with maple type leaves originally from
India. I have grown it in Arnhem Land (northern Australia) and it
produced lots of seedlings (unsolicited). It will also grow in
subtropical conditions, I believe. Neem is used in many human skin
health products and is also used widely as an insecticide and there are
products for pre-treating seeds to discourage seedling eaters that are
OK'd for organic use, I believe. It is a very special tree.
The tea tree is a malelueca species (or leptospermum) as someone pointed
out, used in Australian Indigenous medicine. A number of different
Australian melaleucas grown in a range of conditions had healing
properties and were used by Indigenous peoples. They tend to grow in
wetland or coastal areas. We haven't had success using it for headlice.