VTC

Happened to my 7Sii. Lived with it until the entire menu system wonked out and got both fixed at same time in Sony hospital. Has nothing to do with the removable camera battery. The internal capacitor circuit for D&T isn't doing its job holding a charge on battery swap.

6300 doesn't have the ability to shoot in the Cinetone profile whereas the FX6 does. I believe what you're looking to do is match the look from one camera to that of the other and that could be quite an undertaking if any of the many settings weren't dialed in to match as closely as possible. Gonna be a tricky task especially if the 6 was shooting in Cinetone and the 6300 was shooting in a standard, i.e. non-Log profile.

Don't have access to mine right now but on the 7Sii it's under HDMI Settings. HDMI Info Display. Set to OFF.

Lighting situation. Due to the refresh rate of fluorescent or LED. You won't see this effect outdoors or under incandescent lighting. Can be limited by adjusting shutter speed or frame rate.

Don't understand the inquiry. Looking to MATCH that or IMPROVE that image? (Washed out. Weak contrast. Tepid colors.)

Happen to have a dummy battery so you can run it directly off the mains as a test without having to use a battery at all? (Lousy batt life forced me into using larger capacity batteries externally). Another option is to power the camera via the USB charge socket (internal battery required to try this) and see if you get longer run times. USB isn't sufficient enough to keep up with the power draw but it does extend somewhat normal battery drain. Had multiple batteries tell me there was plenty of charge but cratered sooner than the 67% or whatever charge remaining indicated. Try setting Power Save to OFF and see how long the camera remains on in photo mode then video mode without actually doing either. Power save feature shouldn't enter into this because active recording keeps it from being implemented. Only when nothing's calling on camera resources does it kick into play.

If you shoot video set to a picture profile it affects images as well UNLESS the camera shoots images in SILENT MODE. Then pics aren't affected by the flat looking profile and exposure compensation settings dialed into video mode. (That's been my eperience.)

Yes, no enlarging to check focus in the 7Sii while in video mode but here's what I do to counter that. Picked up an elderly SmallHD DP4 off ebay. $65. It's small, plastic, and very light weight. Use it in Focus Peaking mode, B/W setting. I only need it for framing and focus. The Atomos or Blackmagic get used when I need the benefit of an external recorder but for focusing it's the DP4. The DP6 does the same thing but is larger & therefore heavier & overwhelms the Sony.

This shows what an EVF looks like inside. It also tells of what happens when a camera gets wet. https://www.lensrentals.com/blog/2017/10/about-getting-your-camera-wet-teardown-of-a-salty-sony-a7sii/

Banding due to artificial lighting. You'll never see it in daylight.

There a reason to keep the specific camera model a secret from those trying to help? There's something like 50 different cameras in Sonys alpha corral. Knowing which of the ponies you ride would be a crucial detail worth revealing.

With such a vague, non descriptive question lacking specifics you shouldn't expect anyone to waste their time answering it. .

Had the same problem but it wasn't the dummy. Mine FIRST started with the dummy but soon migrated to EVERY battery swapped out. Lived with that massive inconvenience for a year before I sent the camera in for repair of a wonkified menu system. Though there's no user swappable memory battery there must be an internal one that keeps a wee amount of power keeping things charged when the battery flatlines.

I've come across problematic files that had bad data that wouldn't properly transcode with one program but would with another. Sometimes I needed to use an earlier OS because a more recent OS supplanted some codec versions that worked and the updated codec didn't. Dropbox or something one of the problematic files and I'll run it to see if it's the file itself or some configuration / compatibility issue on your end.