Free-to-use parenting style questionnaire
There are a lot of parenting style questionnaires. Without knowing what dimensions of parenting style are of key interest, how long you want the questionnaire to be (e.g., trade-offs between validity, reliability with ease) and such, it's hard to recommend a particular one. You can see several from the parent perspective here: https://www.google.co.uk/search?q=parenting+style+questionnaire

As to regulations, you may need to contact the authors or journal about whether the scale is permissible for commercial use. I've only ever used scales for academic use.