what are the steps in adaboosting?
Firstly, i want to notice that adaboost is a ensemble of stumps, and each stump is added to the ensemble sequentially, trying to compensate the errors of the existing ensemble. 



Saying that:


In every step you have a new weighted dataset, and the Adaboost algorithm tries to fit a stump that splits the new dataset best. So yes, it is possible, and it does happen, that a single feature is used more than once (but the splitting value calculated by the stump should be different in order to reduce the ensemble's error.)
Stumps' creation is a continuous process, they are calculated in
every step for the new weighted dataset.