MiKTeX is just a distribution of TeX related tools. Few of many: TeX, LaTeX, XeTeX, pdfTeX, pdfLaTeX, luaTeX, luaLaTeX, bibTeX, bibLaTeX, biber,...
It does not contain anything to write .tex files. It does provide one viewer - yap - to preview .dvi files (output from TeX and LaTeX).
IDE is user's taste and user's responsibility. Same as postprocessing. (postscript / pdf).
It is fine you can't find IDE documentation in MiKTeX - it has never been intended to provide any IDE.
After some time you'll recognise there is no One TeX compiler to suit every task. The sooner you give up on such idea, the better for you. Trust me.
Typical compile queue for simple document with citations is:
1. pdfLaTeX - include changes
2. bibLaTeX - update citation references metadata
3. pdfLaTeX - update citation references
4. pdfLaTeX - update page references
This workflow vary from document to document.
Sometimes you are happy with (plain) LaTeX. Sometimes you prefer pdfLaTeX. For other tasks you are looing for XeLaTeX or luaLaTeX. Sometimes you don't need bibLaTeX. Sometimes you want to use makeindex or other packages.
Dedicated (La)TeX IDEs are designed with this in mind. For example, TeXmaker, have F-shortcuts one to run default compiler and preview afterwards, other just to run default compiler, another to run luaLaTeX compiler, another for bibLaTeX, etc.
On the other hand, every IDE has its own shorcut philosophy and keeping in mind whether "compile" is bound to F5, F6, F1 or Ctrl+Enter is irritating.
Other thing is syntax and overall philosophy. TeX is not a programing language. It does not have 'variable' in its core; 'variable' was retrofitted in there. TeX's foundations are character classes and macros. Those are TeX's primitives and averything else is built on it.
From user perspective there is no syntactical difference between macro (\TeX) and length "variable" (\ex).
LaTeX macro name, or command, starts with \. It ends either with the first non-text character (\!, \%,...), or with empty space or non-text character (\section{Foo}, \rm Foo).
Commands are usually single. Paired commands are usually only \begin{Foo}--\end{Foo}, where Foo is called environment, or \if -- \fi interpretation of conditionals.
TeX recognises two 'modes' - text mode and math mode. They behive differently and different command can be used. Some commands are exclusive to one mode or another. For example ^ to introduce upper index is available only in math mode.
All this is covered in all TeX-oriented IDEs. They usually detect default mode switching to highlight math mode. I'm not sure Spyder can do that (easily).
If you want to set your IDE to compile properly, you can download TeXmaker and check it's compiler calls from Preferences... card.
If you decide to go this way, consider writing a blog post about your journey either to show others the way to follow, or (and I'd bet one CZK on it) show others why not to try it.