See my answer for question 1. Start with the HTSM. For understanding the product, the progress, the coverage and what is going on in discussions in your team, there are many models you can use. I recommend to use many models, since every model gives you a different perspective. There is “unfortunately not 1 model to rule them all”. Some examples:
- Requirements
- Technical designs
- Stakeholder overview
- Quality attributes
- Architectural overviews
- Proces models
- Flow charts
- Data models
- Risk models
- Timelines
- Your own product coverage outlines (see my video on product coverage outlines on youtube)
More on models in these blogpost:
- Many models - better test ideas by Rikard Edgren
- How I use modelling in software testing by Anne-Marie Charrett
- Modeling Testing by Jeff Nyman
- Mental Models: The Best Way to Make Intelligent Decisions