About monitors...
1. A 4K TV is still a "monitor".
2. I think you can expect to see differences in the same image on different monitors.
3. (I don't know, but) TVs may be optimised for moving images rather than stills.
General sharpening, etc...
Well, I don't know what you think about the sharpness of my images attached to AP,
but there is a limit to what you can expect from an initially good image.
Certainly, too much re-sampling and sharpening will shake up the image info and
sometimes make it a worse image. For this reason I try to do as little to the image
as possible. You might try along the lines:
-If you can crop away some of the original image, do so, then try a single re-sample
to the desired size in pixels - 1200 on a side. (Yes, it can be SQUARE, so there is no
need to invoke "long" side (or worse, "longest"). Use just "Bicubic" re-sampling,
and do any sharpening afterwards. (Because you're doing a single, controlled action.)
-"Save as..." the result at jpeg quality 10* at first, then, while keeping the file OPEN,
check the file size. If it exceeds the maximum 400KB you will have to decide between
resampling the image down a bit more (say to 1000 pixels), or reducing the jpeg quality
a bit more (upping the file compression) when saving.
NB: If you keep the file open, you can use the History** (of your actions) to go back and
restore the full file info to, say, before the first re-sample. From that point you may try
1000 pixels. Similarly for file compression when saving. If, however, you close the image
and then reopen it, you are reworking previous work.
On other Qs (not in order)...
No/yes/I don't know/only on Fridays after 4 PM...
*Quality 12 (maximum) usually results in pretty big file sizes. At a(n absolute) pinch I have
gone as low as 8, which is the lowest "high" value. You can compress away fairly freely if
your image contains lots of bland monotone, like blue sky, walls, etc, but not when there's
a lot of detail.
**In your PS preferences, set yourself a generous number of history states, like 35-40.