Censored output data, which activation function for the output layer and which loss function to use?
We can't tell you what loss function to use.  That is based on business needs.  In particular, what is the cost of being wrong?  Is the cost of being wrong proportional to relative error?  absolute error?  Something else?  That will drive the choice of loss function.  You should try to choose a loss function where the value of the loss function is proportional to the cost of the error (e.g., the monetary cost to your company).

Using ReLU as the activation function in the final layer would be sensible given that your data is censored to replace all negative outputs with 0.