ARIMA grid search for best p,d,q,P,D,Q order based on BIC metric

i am new to R , and i was hoping to get some answers to some questions i have
1- is there a function to loop through a range of ARIMA model to get the best order/seasonal based on BIC/AIC ?
2- do i have always to difference the data if its not not stationary or there might be another reason to that and i dont have to take the differencing ?
3- i used Auto ARIMA to find the best ARIMA model based on its BIC , and i specifically specified BIC perimeter in the Auto ARIMA function but when i tried to use some candidate ARIMA order i was able to get a lower BIC than what the Auto ARIMA got, how is that possible ?
4- what could be a better practice, to use the differencing time series data in the arima function , or to use the original one and specify that there is an order of d there?

Referred here by Forecasting: Principles and Practice, by Rob J Hyndman and George Athanasopoulos

I've already answered this question at

yes .. thank you so much

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