Colors look washed out when exported. LUT makes it too dark.

Virality did a great job of a quick summary of your first question/problem. Essentially, you are trying to correct color and then view it to check it ... using a non-standard-compliant monitor for video media, and then checking it on an app without correct color management. I'll add in ... with the added issue that the Mac ColorSync utility does not properly apply both the scene and display transforms to much Rec.709 (video) media.

That was why he was referring to viewing video images on a properly calibrated monitor.

The second problem you're having is one of understanding what you can and can't control.

Gramma's Green TV

I work with colorists a lot ... daily. I'm a contributing author for a pro colorist's teaching website. And one of the colorists had a tale to illustrate the problem all colorists face with every project they touch:

Once you have graded and delivered the project/file/program, you have no control whatever over how anyone else on the planet sees it. And no other device will ever show it as you saw it.

The colorist had graded an ad for a major corpoaration to use on broadcast television. He was pretty pleased as it was pretty "hot" for color but stayed within broadcast standards. Then took a vacation to like Wisconsin to visit his Grandmother.

Sitting in her living room talking, the TV was going all the time in the background as some people do. And while it was just 'on', his commercial came up. His Gramma was very impressed even though he was horrified.

What was the difference? Her TV was set way green ... so everything started well into the green. This is her reference ... and within that, his commercial looked like all the other well-produced professional media. His mental reference was of course the very exactly neutral screen he graded it on.

Colorists cannot exactly match their Grade 1 Reference monitor to the large high-end consumer display they use in the same suite, connected to the same signal, and also run through a LUT box to apply a particular calibration for that screen. Most often, they try and setup their suite layout so the client just can't see their reference monitor ... as if the client can, they'll say "Make this screen look like that one ... "... which is ALWAYS a wrong move.

There is way too much variation between screens, to begin with. And color settings and management across platforms, devices and screens is simply a complete uncontrolled mess.

You cannot preview how anyone else will see the image. Get over it. Setup a system to give you a decent and known image quality. Work to the standard. Produce your material.

And publish it, and move on.

It's all any pro colorist can do. And they've got a ton more gear and equipment than you do.

Neil

hey this is a common issue when grading on retina displays - i'm sure you've seen the forums (https://community.adobe.com/t5/premiere-pro/washed-out-colours-when-exporting-as-h264/td-p/9709377?page=1)

and here

https://community.adobe.com/t5/premiere-pro/exported-video-looks-totally-different-on-youtube-than-in-premiere-or-vlc/td-p/10486551?page=1

but basically from what i've seen the only way to completely avoid this is to grade on a calibrated external monitor set to rec709 (not the p3 gamut of the retina display. it has to do with the gamma of the program monitor which is rec709 and the gamma of exported file which is srgb/rec709 (i believe) (at the time i read this) 

without a reference monitor you have to split the difference between what you're seeing and what you want and just realize that even once you get it looking exactly how you want it to look on your monitor, the viewers are going to have completely different setups that looks completely different regardless, and they isn't anything we can do about it.