Question

That’s Vim gives us a list of matched “$ some maths symbles $” when we press some keys after typing just “$” or “$ with more maths”.

Answer 1

My solution (basing on latex-box) for completing inline eqs in either inline env or numbered env

That’s you have typed two eqs, you want to type them for another time:

% two inline eqs
$hello$  $world$

% completion in inline env
$[part of "hello"]<ctrl-x><ctrl-o>

% completion in numbered env, 
% it's still triggered in the same way, but will leave eq without "$"
\begin{equation}
    $[part of "world"]<ctrl-x><ctrl-o>

EDIT1

In the official repo of Latex-box, this functionality is disabled by default.

The switch is let g:LatexBox_complete_inlineMath = 1.