2-channel dimmer from NE555 + LM358?
Yes it only uses one of the op-amps and there are two in the same package.
Assuming your power supply can handle the power drawn from them then yes. As long as you don't hook up the LED strip to the same MOSFET.
Yup, Op-amps have infinite input impedance so they won't effect your circuit.*
I believe the frequency won't be either of the ones you state. However I may be wrong.


\begin{align}
    t_{dicharge} &amp;= (0.693 * C3 * R2 * R3) \\
    t_{discharge} &amp;= (0.693 * 2 * R2)
 \end{align} 

adding them together 

\begin{align}
    T &amp;= 0.693 * C3 * (R3 + 2*R2)
 \end{align} 

convert to frequecny

\begin{align}
    F &amp;= \frac{1}{T} = \frac{1}{(0.693  C3  (R3 + 2R2))}
 \end{align} 

*Well, high enough that it shouldn't effect your case.