There's NCA (drones), NMC (laptops, phones, many electric cars), LFP (stationary/grid), and LFMP (many new electric cars; slightly more expensive but higher current variant of LFP).

Yes, this happens sometimes.

Search this page for "PTC": https://www.electricbike.com/inside-18650-cell/

The PTC protects the rest of the battery if a single cell internally fails short.