Former supervisor authorship
I don't think this case warrants authorship. Your advisor did nothing to contribute to the new work, helping you with a prior paper says nothing about future papers. 

You should absolutely cite your thesis (or whatever paper used this dataset) in your new work, and make sure that the dataset is not protected in some way (say, if it's a clinical dataset that is restricted in use via an IRB you might not be able to use it).