What process(s) writes to ALERT log file in Oracle?
Any process can write in the alert log.
Even you can write in the alert log using the PL/SQL DBMS_SYSTEM package.
Trace file names clearly indicate which process they belong to. Trace files are named like ORCL_smon_1234.trc, where ORCL is the name of the instance, smon is the name of the server process, 1234 is the OS PID of the process.