# ML model to forecast time series data

This question has three sub-parts, answering each of which probably doesn't require huge text. I hope that is okay.

I'm trying to understand time series prediction using ML. I have the target variable $$y_t$$, and suppose two other variables $$x_t,z_t$$ (e.g. if $$y_t$$ were the demand of an item, $$x_t$$ could be type of item or price of item, etc.). Also, let's say I'm using a random forest model because I've read it generally does okay out of the box.

i) From my understanding, if I include $$y_{t-1}$$ as a predictor, the model may just learn to predict $$y_t=y_{t-1}$$, for example there is autocorrelation with lag $$1$$. Given that, is it a bad idea to include $$y_{t-1}$$ as a feature?

ii) Each of the predictors $$x_t,z_t$$ may have one or the other typical time series characteristics, like non-stationarity, autocorrelation or seasonality. Is there some special method I have to follow or transformation (to the predictor) that I have to do if any of the predictors has any special characteristic?

iii) Typically, what are some best practices to go about such forecasting? My current thought is: use $$x_t,z_t$$ as predictors without transformation. Use ARIMA with grid searched parameters to fit the training data and validate. Use that as baseline. Finally, use random forest to predict the differenced time series $$y_t-y_{t-1}$$ using $$x_{t-1},z_{t-1}$$ as predictors and compare to baseline. Am I missing anything here or should I consider something additional?