I am working on a time series forecasting project using LSTM with monthly sales data. I have already applied differencing to the sales data to stabilize the mean. Now, I am considering adding seasonal features to improve my model's performance. However, I am unsure whether I should apply the seasonal features directly to the differenced data or create new seasonal features from the original data before differencing.

$1,$ In my LSTM model for forecasting monthly sales, should I apply seasonal features directly to the differenced data, or is it better to create new seasonal features from the original data before applying differencing?

$2,$ After making predictions with my LSTM model, how do I revert the differenced predictions back to the original scale, especially if I have used seasonal features? What steps should I take to calculate RMSE accurately in this context?

$3,$ By incorporating multiple features like seasonal indicators and moving averages into my LSTM model, does this change my analysis from a univariate to a multivariate time series problem? What are the implications of this change for my modeling approach?

Can you provide a step$-$by$-$step process for implementing an LSTM model for my time series forecasting project, including how to handle differencing, feature engineering, model training, and evaluation