The "shadow" area of the Moon is lit by Earthshine - light reflected towards the moon from the sunlit part of the Earth. From the Moon's point of view, the more of the earth that's sunlit, the brighter the earthshine is.

If you think about the Sun-Moon-Earth geometry, the thinner the crescent moon is as seen from Earth, the larger the lit area of the Earth gets as seen from the moon. So the thinner the crescent, the better lit the "shadow" part of the Moon is.

So try taking shots with the thinnest crescent you can manage. And keep increasing the exposure until you see some detail in the shadow area - that can be a LOT longer than a normal moon photo.

It's possible the image you've picked might be a composite - sometimes the lit part of the moon is so overexposed it bleeds into surrounding pixels and looks noticeably fatter than the rest of the moon. Or the shadow brightness may have been boosted in post processing.

Not sure about the Venus starburst - it might be from a lens with a 7 bladed aperture iris, or, as you suggest, a starburst filter (though 4 or 8 ray versions are probably more common). This is one of the things that makes me think the image might be a composite - if you look at the length of the rays from Venus, then you'd expect the light from the brightly lit part of the moon would be spread out by a similar amount, and that doesn't appear to be happening. (It could also just be that Venus, being closer to the sun and with more reflective clouds, is actually brighter than the dark gray moonrock, so the fact that both venus and the brightly lit moon are both maxed out in the photo is misleading - in reality, venus may have a higher surface brightness, producing brighter and longer diffraction spikes.)