9.79.3 Can you answer these questions?

9.79.3.1 textcolor and displaystyle

https://tex.stackexchange.com/landing/r/digest?cta=question&id=702297

I need to color a portion of a displayed equation, but when I do that the equation gets turned into \textstyle instead of \displaystyle.  Here is a minimal working example: 
\documentclass{amsart} 
\... 
[equations] [color] [displaystyle]
 

asked by underflow https://tex.stackexchange.com/landing/r/digest?cta=user&id=183182 Score of 1

9.79.3.2 Unable to use latest release of miktex.exe on windows 10

https://tex.stackexchange.com/landing/r/digest?cta=question&id=702289

ERROR DETAILS 
Program: miktex.exe 
Error: The executed process did not succeed. 
Details: 
fileName: C:\Users\vs\AppData\Local\Programs\MiKTeX\miktex\bin\x64\miktex.exe 
exitCode: 1 
[miktex] [windows]
 

asked by Birdy https://tex.stackexchange.com/landing/r/digest?cta=user&id=80252 Score of 1

9.79.3.3 Heatmap in Table from green to yellow to red using pgfplots/pgfplotstable

https://tex.stackexchange.com/landing/r/digest?cta=question&id=702113

I am currently working my way through one error to another. What I want to create: 
So in essence a table with color coded cells that gradually fade from red to yellow to dark green. Ideally, in each ... 
[tables] [pgfplots] [pgfplotstable]
 

asked by Alex_qp https://tex.stackexchange.com/landing/r/digest?cta=user&id=274228 Score of 1