Can I use categorical data and Decision Trees to regress a continuous variable?
Yes, most software implementations of trees will allow you to predict a continuous target variable with all binary predictors. This is because the predictors are only used as splits, and the prediction comes from the average value at a given terminal node. The predictions will not be truly continuous across all terminal nodes in the same way that linear regression is continuous, but in practice, this is generally not a problem. If your tree is under-fitting (not continuous enough) you can always add more terminal nodes. Also, one-hot encoding should be sufficient.