which forecasting models could be chosen?
Should the data be considered as a multidimensional time series?


This depends on whether the target variable (the one that you want to predict) depends on the others. If not, there is no point in doing it. A fast way of checking if the variables are linearly dependent and, therefore, multidimensional forecasting is meaningful is by checking the linear correlation of the variables. Then select only the variables that have high correlation (>0.5) with the target variable to include them in your prediction model.


  I am still thinking which methods, techniques can be chosen.


The model that I recommend for time series forecasting is a Recurrent Neural Network. This is because of its inherent ability to store previous timesteps in its memory and to incorporate them into future predictions. This is very important, because it is among the few approaches that exploit the temporal dependencies between samples.


  I'm currently looking into the direction of some kind of neural
  network and implementation in python (but I still don’t know which
  package).


The most convenient way of implementing a recurrent neural network in Python is by utilizing the Keras framework. Please go carefully through this tutorial, as it will definitely be a very good first step to attack your problem.