Take home had 3 parts, one about product usability test and proposing improvements as well as prioritizing those improvements. Second part was about deciding if a company should implement, integrate or discard a set of features. Finally some A/B testing questions.
Interviews were mostly about past experiences, but also included some open ended technical questions you would expect for a Product Management position like "given this product and it's features, which are the main risks you identify", or "how would you prioritize the following features".
