Sorry, I'm using a translator, which causes my statements may not make sense sometimes.
When a player uses TNT or fire to destroy something, CoreProtect will only record #tnt or #fire, is it possible to record both the player who lit the tnt/fire?

You can lookup for user placing tnt or fire

You can lookup for user placing tnt or fire

How? Block by block?

e.g. /co lookup action:+block include:tnt time:1d radius:50 (you may need to change time and radius)
You can also do radius:#global or radius:#world if you don't have a lot of players that would place tnt.
For the fire you should also add exclude:#fire so you don't get spammed with #fire placed fire (e.g. /co lookup action:+block include:fire time:1d radius:50 exclude:#fire

Thanks!