When reducing from HALT, can you create a Turing machine that asks whether a simulation stops?
No, you can't.

First, as a technical point, it never makes sense to say "If this simulation halts", since that would require doing the whole simulation and, if it doesn't halt, you'd never finish simulating it. You can, in certain circumstances, ask whether a particular Turing machine halts on a particular input, but that's something subtly different.

But the main point is that your reduction looks backwards. You're supposed to be using the argument "$S$ must be undecidable because I could use the ability to decide&nbsp;$S$ to let me decide the halting problem, which is impossible." But, by basing decisions on whether some Turing machine halts or not, you're assuming that you can determine this, i.e., assuming that you can already decide the halting problem.