Final answer:
The nail disorder where the nail grows into the skin causing ingrown toenails is Onychocryptosis. The nail bed is furthest from the nail growth center, and a fungal infection affecting nails and skin is classified as systemic mycosis.
Step-by-step explanation:
The disorder in which the nail grows into the edge of the nail grooves, causing ingrown toenails, is called Onychocryptosis. This condition occurs when the edge of the nail digs into the skin of the toe, which can be painful and lead to infection. The other terms provided refer to different nail conditions: Onychauxis is the thickening of the nail; Leuconychia is white spots on the nails; and Onychogryposis is a nail disease with a curve much like a ram's horn.
Addressing the question about nail growth, the part of the nail furthest from the nail growth center is the nail bed, which is the skin beneath the nail plate. The nail root is at the proximal end of the nail and is where the nail begins its growth. Lastly, a fungal infection that affects nails and skin is classified as systemic mycosis.