How can I connect my iMac (27"-inch, Late 2012) running on Mojave as a second monitor to my MacBook Air (13-inch, Early 2015) running on Mojave? I have connected them using a Thunderbolt 3 cable but am not able to see mirroring option in Display Set

You can't. The display part of Target Display mode requires a Mac running High Sierra or earlier.

Use your iMac as a display with target display mode - Apple Support

****....there’s no loophole/hack?

If there is, nobody could discuss it here.

Is there any other option for a second display, even if it’s a totally separate monitor?

Sure, just plug one into the Air. You might need an adaptor to go from your Thunderbolt 2 port (Thunderbolt or Mini DisplayPort) to whatever input the monitor has (DVI, HDMI, VGA). It will support one external display up to 3840x2160 (4K).