k-Nearest Neighbours with time series data - how to obtain whole-time-period estimators
Do you have more numeric features? KNN works off distances (euclidean, L1, etc.) which requires numeric data. It doesn't take in categorical data. Your activity feature will not work with KNN and even converting the date to say an integer will just create a time series which will not perform well with KNN. I think your approaching this wrong. Try logistic regression. It will take in both categorical and numeric features. 


  There is no particular value in keeping Team and Shift separate, so I should create a joined column which combines both.


I would build two separate models for team and shift. You'll get higher accuracy because your using the data to predict less classes and letting the models specialize on each task.

Overall I would use logistic regression not KNN. It's more appropriate for your problem. Hope this helps.