To send you down the rabbit hole on your journey to learn about moving averages, read "Rocket Science for Traders", by John Ehlers. The TL,DR version is that moving averages are lowpass digital filters. The two fundamental types are finite impulse response (FIR) and infinite impulse response (IIR). The important question of weather or not they work is both yes and no, though I tend to lean toward no. Good luck on your journey of discovery!
First, it depends upon your trading timeframe. It needs to be precise enough to give information but not to coarse to gloss over things. Also it depends upon what you use it for, e.g. Signals or actual order generation. BTW: They are not the same thing, or at least should not be unless that is by design. If this is news, then figure it out how these two different actions triggers work in your system. AND as everyone above says, it is easy to use it wrong-poorly. For example, using it for real-time decisions is a terrible idea. Worse to use it to justify things that should not be done. But to use it as a historical reference, it has its uses. Hope that helps.
%% YES; including but not limited to 50dma+ 200dma. Applies to ETFs like SPY,VOO + QQQ...... not forex. I dont use any ma for cash copper/metals business. Good question.