How to evaluate/improve the accuracy from the prediction from a neural network with an unbalanced dataset?
It all depends on your dataset. Neural network are not magical tools that can learn everything and also they require a lot of data compared to traditional machine learning models. In case of MLP, making a model extremely complex by adding a lot of layers is never a good idea as it makes the model more complex, slow and can lead to overfitting as well. Learning rate is an important factor as it is used to find the best solution for the model. A model makes mistakes and learns from it and the speed of learning is controlled by learning rate. If learning rate is too small, your model will take a long time to reach the best possible stage but if it is too high the model might just skip the best stage. The choice of activation function is again dependent on the use case and the data but for simpler datasets, activation function will not make a huge differnece.
In traditional deep learning models, a neural network is build up of several layers which might not always be dense. All the layers in MLP as dense i.e. feed forward. To improve your model, you can try a combination of dense layers along with cnn, rnn, lstm, gru or other layers. Which layer to use depends completely on your dataset. If you are using a very simple dataset for a school project, then experiment with traditional machine learning methods like random forest as you might get better results.
If you want to stick to neural nets, read about other types of layers, dropout, regularization, pooling, etc.
I used gridsearchcv to determine which hyperparameters in the mlpclassifier can make the accuracy from my neural network higher. I figured out that the amount of layers and nodes makes a difference but I'm trying to figure out which other configurations can make a difference in accuracy (F1 score actualy). But from my experience it lookes like parameters like "activation", "learning_rate", "solver" don't really change anything. 
I need to do a research on which other hyperparameters can make a difference in the accuracy from predictions via the neural network. 
Does someone have some tips/ideas on which parameters different from the amount of layers / nodes that can make a difference in the accuracy from my neural network predictions?