How to track the execution of background functions in WORDPRESS?

Question

WordPress

Hello.
I use self-written processing to load goods from 1C to woocommerce. The created XML file in 1C is loaded into WORDPRESS as media files. Then, through AJAX, the function that is located in functions.php is launched. This function modifies product records in woocommerce. The function works in the background and for a long time. There are no problems on the local server.
I have noticed that it is possible to run multiple downloads and processing. There were questions:
How to monitor the work of such functions.
Interrupt.
Determine if they were successful. On the host, processing did not always end successfully. With the same incoming file, processing could reach the end or stop. Perhaps some kind of conflicts on simultaneous access to data.
Is it possible to see the log of work and errors.