Earlier quoted context omitted.
In theory, yes. Of course in practice, it's not so bad: they can run the parser in a different thread, they can put hard limits on how long they run, etc. (The hard limit is how C++ gets parsed, I think. Since parsing C++ is also undecidable thanks to weird interactions with template metaprogramming.)
Yes, templates are turing complete. https://github.com/knome/metabrainfuck/blob/master/bf.cpp Does attempting to autocomplete such a template cause issues for IDEs? I used emacs when writing it, so I've never tested such a thing.
For C++ even precise syntax colouring would be undecidable---and just hard to get the logic right. There are two ways out: (1) implement an approximation and the occasional impression, (2) ask the compiler for help. I think the llvm project helps with the latter.
(What does emacs have to do with things? Or do you mean you are using emacs without any special support for C++? With the right modes you can turn your emacs (or vim etc) into basically a fully fledged IDE.)