on youtube on the sony alpha lab there is a guy named Jay that has a bunch of very good youtube videos on the many complicated menu selections focus and exposure suggestions. I have an m3 and also an m7 and used his videos to help me understand and better utilize the focus areas and methods. also gary freidman archives has e books for every model of the rx100 which will help you immensely...

nice photo- here is my attempt at an edit. Thanks for posting

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Here is a layman's explanation of flash duration.
1, Your camera has a sync speed anywhere from 1/160 sec to 1/320 sec. This is the shutterspeed max to avoid shadows (of the shutter closing) on your sensor it ensures that the shutter can fully open and close
2. The actual flash duration is way faster than that (in the vicinity of 1/10000 sec and controlled largely by the power setting on your flash ie 1/1 full power *longer duration) --- 1/128 very low power and shorter duration. The brightness of the flash is consistent and the power setting changes the duration of the flash.
3. TTL measures the effect of the light on your subject and when enough light it stops the flash again this is done by increasing or deceasing the power which changes the flash duration
4. HSS (High speed sync) Many cameras and flash systems have this feature which effectively allow shutter speeds up to the max on your camera usually 1/8000 of a second. this is done by pulsing the flash to ensure each exposed segment of the sensor (not covered by the shutter movement) is lit and exposed.

you can set up an import preset and save it and then specify it in future imports. go through all your import panels on the right pick the settings you typically use and then go to the bottom of the screen you will see a black ribbon and on the right of the black ribbon little up and down arrows click the down arrow and save your settings as a preset... Or pick a preset that already exists with the settings you like..

nice scene thanks for posting.. Here is a crack at editing it.

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I use photophoto color space in lightroom (the default) and have set my PS colorspace to prophoto as well. When I export photos out of lightroom for posting elsewhere I use jpg which cuts it back to 8 bit and srgb. Pro prophoto is probably overkill as most of our monitors can not detect the subtle difference in tone, shades and brightness but it still captures and utilizes the maximum and widest range of colors, shades, tones, etc

First, I find a bunch of erroneous information here by people who want to help.. So let's straighten this out.
the first place to start is in Lightroom preferences and the external editing tab. This is where you set up how your files look for file format either psd or tiff are suggested, color space I use prophoto which is lightrooms default but not PS default and then 16 bit bit depth NOW DOWN AT THE BOTTOM CHECK STACK WITH ORIGINAL AND PUT SOME IDENTIFYING TEXT IN THE CUSTOM TEXT FIELD (I use edited in PS.. Your process was fine until you did a save with rename of the file. JUST DO A SAVE AND CLOSE and PS will insert the custom text into the file name and send it back to lightroom right next to the original(s) assuming you are ordered by capture time. In addition, if you first edit in lightroom you will get a pop up screen to ask if you want to send it to PS with the lightroom edits or as the original raw file.. My process I send it with lightroom edits it comes back to lightroom and I can then make additional edits in lightroom on the PS edited image. You can even send it back to PS again (THIS TIME choose as original), edit it in PS a 2nd time and then return it to lightroom updated with the PS 2nd edit and the lightroom wnd edits intact. I hope this helps... Lastly the color shifts are likely due to mismatched color space between lightroom and PS

A different light!!!

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I upgraded my rx100 m3 to the m7 the extra range makes all the difference and being ble to track and take 20 frames per second make a big enough difference.

An alternative you can try is using a slow shutter with a flash set on rear curtain sync the flash will freeze the action and leave a trail of motion blur behind the moving subject

Are you able to format the card in camera? Can you access the card and read it from a computer?

the second image has a much stronger subject (the water fall). However the bright sky steals the viewers eye and I agree that cropping it out will further emphasis the strong subject. If you are allowed to post process the water in the water falls could be brightened ever so slightly to add even further emphasis.

I too am a fan of the sony rx 100 I started with the m3 and just bought the m7 with the 24-200 zoom it also has very fast focus and can shoot action shots at 20 frames per second with great focus tracking. I too bought it to avoid taking the big camera and multiple lenses on trips. This camera can shoot raw and full manual but also has can be put in auto or any of the other shooting modes PASM. It has a !" 20 meg sensor and takes an excellent photo. I have some landscape shots I've enlarged to 16 x 24 and printed on metal and they are beautiful.. It is however, not cheap to buy.

a lake or the ocean make it a houseboat floating on water..

works for me... love this shot!