Using MinionPro for the main font and Fontspec for the monospaced font

I suggest you load MinionPro with onlymath option. As far as I understand it, MnSymbol is mainly used for math.

Use \setmainfont of fontspec to set Minion Pro As the math font. The problem with all caps and small caps is because MinionPro optimized the spacing while fontspec won't do it for you automatically. But the solution is simple, use \addfontfeatures{WordSpace=...} feature of fontspec. Also Kerning=Uppercase will enable the cpsp opentype feature though I don't find its space is enough for all caps title.

Indeed I used MinionPro package for quite a long time. But the only reason stopped me for switching to fontspec before is the lack of support of microtype in xetex. Now I use fontspec and LuaTeX exclusively. This is a better solution than MininonPro since you can access features like case easily, which will select right punctuations when typeset in all caps. And much more.

For Minion Pro font, however, I found that it has a few problems with fontspec. At least on my Mac, there are issues for fontspec to select correct weight and optical sizes. See https://github.com/wspr/fontspec/issues/105.

In my case the medium weight cause fontspec or luatex confused. So I added the following to otfl-blacklist.cnf.

MinionPro-Medium.otf
MinionPro-MediumCapt.otf
MinionPro-MediumSubh.otf
MinionPro-MediumDisp.otf

And used the following to setup my fonts to get correct optical size.

\setmainfont[
SizeFeatures = {
  {Size =     -8.41, OpticalSize = 8},
  {Size = 8.41-13.1, OpticalSize = 11},
  {Size = 13.1-20.0, OpticalSize = 19},
  {Size = 20.0-,     OpticalSize = 72}},
Ligatures          = {Required, Common, Contextual, TeX},
Numbers            = {OldStyle, Proportional},
RawFeature         = {expansion  = default},
UprightFeatures    = {RawFeature = {protrusion = mnr}},
BoldFeatures       = {RawFeature = {protrusion = mnrb}},
ItalicFeatures     = {RawFeature = {protrusion = mni}},
BoldItalicFeatures = {RawFeature = {protrusion = mnib}}
]{Minion Pro}

where mnr, mnrb, etc are protrusion settings I wrote based on MinionPro package's

You can try the mathspec package:

\documentclass[a4paper]{article}
\usepackage{amsmath}
\usepackage{mathspec}
\setmathfont(Digits,Latin,Greek){Minion Pro}
\setmainfont{Minion Pro}
\setmonofont{Inconsolata}
\usepackage{MnSymbol}
\begin{document}

a$\alpha\sum b=c$\texttt{aaa}
\end{document}

I didn't do extensive tests, however.