Using LSTMs for continous learning and predicting
To answer your questions in order:


The whole point of LSTM (or any time series model) is to predict previously unseen values. If states are not reset - then there is a risk of data leakage - whereby forecasts from the training set will lead into the test set. This would mean that your model would perform quite well on the existing set of data - but would perform badly on new/unseen data. This defeats the purpose of implementing a time series model.
Depending on how similar the pattern is, it might be an option. However, it is just my personal experience that LSTMs are not particularly effective at forecasting commodity prices - the main reason being that these models tend to carry forward too much volatility in the forecasts, which tends to interfere with the overall trend of the data. Here is an example of the use of LSTMs in forecasting oil prices, which you might find of interest: Are LSTMs Always Effective At Time Series Analysis? A Case Study of Oil Prices