Diagnostic Test needed for ARMAX Model Specification

Question

I'm trying to fit an ARMAX model using forecast::Arima() which is using MLE (https://otexts.com/fpp3/arima-estimation.html). Thus, there is no need for normality test as required by OLS estimator. I also applied unit root test using ADF.test() on every time series variables included in the model.

My Question is,

1. How do I conducted heteroscedaticity test for MLE estimator residuals?
2. When I run below code to test for auto-correlations

Box.test(na.omit(r11x), lag = 1, type = "Ljung-Box") # r11x is residuals of ARMA(1,1)-X fit
Box-Ljung test

data:  na.omit(r11x)
X-squared = 0.94702, df = 1, p-value = 0.3305

means that there is no auto-correlation.

But.. when I specify the lag > 6, the test show that the auto-correlation existed.

Box.test(na.omit(r11x), lag = 7, type = "Ljung-Box") # r11x is residuals of ARMA(1,1)-X 

Box-Ljung test

data:  na.omit(r11x)
X-squared = 22.508, df = 7, p-value = 0.002076

Last, is there any other diagnostic test to be conducted?