ac6000cw

I use exactly that lens (Nikon mount) + cheap Camdiox speed booster on a Pana G6 - works fine as the equivalent of a 12-36mm f2 lens, and that speed booster does have a aperture control ring for Nikon 'G' lenses. Main downsides of the combo is that all the glass makes the camera very front heavy and there is no stabilisation. The other cheap M43 low-light lens option is the Pana 20mm F1.7 (lots around used as it's quite an old lens now), which works well but the autofocus is slow and a bit noisy.

​No, it's the successor to the FZ200 - note the small sensor size (1/2.3")

​There is some info on the 4K cropping/downscaling in the 'preview' here - http://www.cameralabs.com/reviews/Panasonic_Lumix_G7/

I agree with Vesku - there seems to be no good reason for not showing the iso/aperture/ss info. It's really useful to know in bright conditions if you should be thinking about using an ND filter, for example. To take another Panasonic camera, the little LX7 (in creative movie mode) does show this information when you half-press the shutter button. On the G6 (for example) I can work around this lack of information when using the 'flicker reduction' option to fix the shutter speed (which essentially gives you a limited video shutter priority auto mode). I set the main dial to shutter priority and the shutter speed to the same as the 'flicker reduction' setting. Then half-pressing the shutter button will show the exposure info (for an equivalent still shot). But you shouldn't really need to do this to get the exposure values....

The effect sounds like the auto wind-cut filter may be kicking in - make sure it's disabled in the menus.

​I'll don't actually own a GX7, just G5 and G6, but on the G6 that is certainly true for Creative Video mode 'S' (and is a real pain), but it certainly seems to behave differently i.e. have smoother exposure transitions, when using normal 'auto' (not iA/iA+) plus 'flickr decrease' with at least some Panasonic lenses (the 14-42 Power Zoom lens in particular). I've never understood why Panasonic don't just offer at least variable, stepless auto-ISO in Creative Video mode - ISO adjustment is basically just video gain adjustment anyway, so why is it so difficult ? (the range could be limited if need be to say -/+ 2 stops - that would cater for many situations)

​Look for the 'Flkr Decrease' option in the Motion Picture menus - that basically fixes the shutter speed to whatever you set it to (normally 1/100 second for 50p video i.e. '180 degree' shutter) when you shoot video in everything except iA, iA+, or Creative Video modes e.g. P, A, S, M modes on the top mode dial are fine. The only other way of doing it is to use Creative Video mode and select Shutter Priority (and set it to 1/100 again). As others have said, if you do this, in very bright conditions you might need to use an ND (neutral density) filter on the front of the lens to stop the video being over-exposed because the camera can't reduce the lens aperture and ISO enough.

I don't know if there is a good de-banding filter available for it, but VirtualDub with the FFMPEG input plugin added will open most video files, and if you install the free GoPro Studio software to get the Cineform AVI codecs, you can export from VirtualDub to a Cineform AVI file (which open fine in Vegas). Avisynth - http://avisynth.nl/index.php/Getting_started - (which is basically a powerful scripting language designed for processing video files) does have some debanding filters available, and can be used in conjunction with VirtualDub (and any other software that knows how to open .avs files) to do very complex processing on a file.

.....and Samsung are one of the largest designers and manufacturers of semiconductors in the world (2nd behind Intel) - you are seeing the effect of that in the image sensor and image processing performance of the NX1. In the 35 years I've worked as an electronics engineer, I've seen Samsung grow from nowhere to being within reach of overtaking Intel in terms of semiconductor sales, so I've no doubt they could cause serious problems for Canon and Nikon (at the very least). And in case you think that is unlikely, once upon a time Canon and Nikon were the 'new kids on the block' with a better product and hungry for market share....

I guess another consideration might be the level of video shooting experience - something like a GH3 (sticking with cameras inside the OPs stated budget) is a lot less likely to bite you with moire and aliasing problems if you get it a bit wrong. And mirrorless cameras have a viewfinder usable for video... Also if you have to do 'run and gun' documentary stuff, a camera and lenses that can do a decent job in full auto mode might be useful - pressing the 'iA' button followed by 'record' has got me footage of events that would have gone away if I'd had to spend time setting it up manually. (but these a just my thoughts as an amateur )

​....and you could buy two of those in almost new condition for £500, or one and a good used lens - the G6 is an underrated camera, it's got some features (like focus peaking) that the GH3 doesn't even have. Unfortunately the GH4 is well beyond the budget of the OP. In low light with the G6, I use a second-hand Tamron 17-50mm F2.8 (non-VR, Nikon fit) on a cheap Camdiox focal reducer to get the equivalent of a 12-35mm F2.0 zoom - total cost about £220, and it's easy to manually focus with the aid of focus peaking.