Turn * into thin space for clearer math spacing

\begingroup\lccode`\~=`\*\lowercase{\endgroup\def~}{\,}
\AtBeginDocument{\mathcode`\*="8000 }

But, regarding the differential, I would use a macro

\newcommand*\dif{\mathop{}\!d}

So you would write

$a x + b$ vs $a * x + b$ and $y dx$ vs $y \dif x$

You might be interested in my answer to Automatic spacing of symbols . Here is it again:

\mathcode`\*="8000
{\catcode`\*=\active
\gdef*{\mathclose{}\,\mathopen{}}}

Compare

$a*b$ 
$a b$ 
$a\,b$
$a*\cos b$
$a \cos b$
$a\,\cos b$

The \mathopen{} avoids inserting two thin spaces if * is in front of a \mathop.