One must have return ticket at immigration. Do immigration official check return ticket status, whether it is cancelled or not?
Do they? Usually not.
Can they? Yes. If you’ve presented concerns that you may not have been truthful or that you may have immigration or other intent, then immigration officers have very broad powers - including verifying your itinerary with airline, hotels, your receiving party, your workplace, etc.
Their computer may or may not have a direct link to the airline ticketing systems, but it’s easy enough for them to verify by phoning the airline.
If you’re at any risk for this, buy a refundable ticket that you can cancel at any time or date such as after you’ve entered. Or simply don’t lie to immigration officers. Lying to an immigration officer can lead to a multi-year or lifetime ban.