XGBoost most important features appear in multiple trees multiple times
To your questions:


It can be normal. 
Features itself are not responsible for overfitting. It can be noise from them or just correlation without causation. I.e. Feature correlates in the training set, but not in the test set. Overfitting is related to models.
Maybe you still don't have a feature that would improve your model significantly. It's hard to say with such limited information. You need to try some experiments with feature selection.