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Electricity prices strongly depend on seasonality of different time scales, therefore any forecasting of electricity prices has to account for it. Neural networks have proven successful in short-term price-forecasting, but complicated architectures like LSTM are used to integrate the seasonal behaviour. This paper shows that simple neural network architectures like DNNs with an embedding layer for seasonality information can generate a competitive forecast. The embedding-based processing of calendar information additionally opens up new applications for neural networks in electricity trading, such as the generation of price forward curves. Besides the theoretical foundation, this paper also provides an empirical multi-year study on the German electricity market for both applications and derives economical insights from the embedding layer. The study shows that in short-term price-forecasting the mean absolute error of the proposed neural networks with an embedding layer is better than the LSTM and time-series benchmark models and even slightly better as our best benchmark model with a sophisticated hyperparameter optimization. The results are supported by a statistical analysis using Friedman and Holm's tests.