I own and have used a DMC-G3. I'm very VERY surprised to hear a claim that anyone's rated it "the best" at low light. It's good at low light; but not great (I also shoot a full-frame dSLR). It's a mid-grade for mirrorless and four-thirds format, which puts it on a par, handling-wise and image-quality wise, with entry-level APS-C dSLRs. I loved mine; it's a great little camera, very versatile, and a giant step up from a 1/2.3" format-sensored compact and a fantastic return on cost (I think they're going used in the $150 neighborhood), but it is not a high-end camera or a whiz at low light compared to other interchangeable lens cameras.

Panasonic doesn't really build tethering capability into its cameras. And as an older model, the G3 has no Wi-Fi capabilities. You're basically out of luck looking for this feature with this camera.

You may want to consider looking at a newer model with wi-fi capability (e.g., the DMC-G6 or the DMC-GX7). While it's not exactly the same as tethered shooting, if what you're looking for is remote control over the camera, or transferring the images directly from the camera to a smart phone or tablet, then Panasonic's Image app on a smart phone or tablet, and the wi-fi capability that's built into newer Panasonic models may accomplish what you want.