When and why is the SELCAL (Selective Calling Radio System) check being performed? When and in what scenario is the SELCAL (Selective Calling Radio System)  check being performed by crew?
If you are unsure whether your SELCAL equipment is properly working, you can request a SELCAL check on a HF-enabled radio frequency. The ATC unit will send out your SELCAL code for testing purposes.

I'm not sure my selcal unit is working, is there anywhere I can test it?
Yes, several places.  If you are located in:

Europe or east of 30W on the North Atlantic, call Stockholm Radio
Eastern USA/Canada or west of 30W on the North Atlantic, call New York ARINC
Western USA/Canada or Pacific, call San Francisco ARINC
Asia - daylight hours, call Singapore or Manila Radio on 8942 KHz USB

[...] All selcal checks are free of charge - just call the station with the aircraft registration mark and when you receive a reply ask for a selcal check and give your selcal code.  The operator will send out your selcal tone and - assuming the selcal unit is working - you will hear a chime in the cockpit.  Acknowledge by replying 'selcal check okay' and you're done!   If your selcal check doesn't work the first time it is worthwhile asking for a 'double' which means you get 2 sets of tones sent out back-to-back and often cures any issues.
(Source: www.selcalweb.co.uk)