Two questions:
You have three questions.
1) How do I choose the output capacitor so that I can drive speakers as low as 4R?
2) What is the logic and the calculation for choosing such value?
The output reactance should be a fraction of the load impedance both for good low frequency response and to limit distortion products. In lower performance applications, the output capacitor may be used to set the low frequency cutoff.
Because of the low impedances and frequencies involved, output capacitors are big and for this reason some designs take feedback *after* the output capacitor so that a smaller one may be used.
3) I saw some designs have capacitors in the feedback loop. Do I need any? Why?
A feedback capacitor is used to limit bandwidth however it has the side effect of extending recovery from clipping which may be undesirable so bandwidth should be limited in other ways. A feedback capacitor also requires unity gain stability from the amplifier which further limits performance.
A series capacitor may be used to reduce gain at low frequency and remove DC offset. Note that the same rule mentioned about about fraction of the reactance to limit distortion applies here also.