In response to Question 1:
The author of the article you mentioned probably used the ts_log_diff transformations to show the forecasting examples because this the most common transformation for most data sets (i.e most generalizable).
EDIT:
It is my understanding that the ARIMA models are used in cases where stationarity cannot be achieved as the author has pointed out in the original post in Section 5: Forecasting a Time Series:
"A series with significant dependence among values. In this case we need to use some statistical models like ARIMA to forecast the data."