Deep Learning with Time Series Data (containing Log Returns)

I am curious about how I would begin to approach this problem. I am working with a time series multi-indexed data frame (consisting of precomputed log returns) of various stocks. In this dataframe, the ticks are 1 second each and I have 300 ticks of each stock (5 minutes). One of the things that I would like the neural network to accomplish is being able to predict the movement of the next 5 minutes of log returns. In doing so, I would like the neural network to predict the volatility of each stock. Is it reasonable to expect my neural network to do this given that I am trying to predict the volatility of each stock of the next 5 minutes? Or is there a better way around this?

If my original suspicion is reasonable, then I would like to use ReLu activation functions for each node in the hidden layers. However, there is an issue with this as it's possible that the neural network can output many 0's (given the nature of ReLu). Would there be a way around this issue?

Finally, I am also curious about the way I am going about with this model of predicting the volatility. In my mind's eye, I figured that I could simply use the Time Series Data feature for the neural network to predict with and use other models to work on other features and later ensemble them to output a final prediction. Would this be the right approach to such a problem?

Thank you so much in advance!