Not always.

Your explanation is not sufficient to take the log transformation. For a positive time series data, taking log may help to achive the normal assumption on residual.

First job is to make the time series stationary. So appropriate differencing comes first. In pure AR or MA looking at ACF/PACF help. Otherwise you need to do some iteration to get p & q.

Refer q3. For a smaller lag of AR and MA one can form pattern. for larger lag of p & q ACF/PACF relationship is complex.

5.If I think the process is stationary, that means my D value = 0?

Correct.