That looks like a nice list of topics for divinations with Da Liu Ren. May I suggest these popular case categories based on my experience with practising Liu Yao:
- 官司 lawsuit or litigation. An example is this divination: Case study
- 失物 lost item. An example is this divination: Will I receive the book?
- 工作 career. For me, this is one of the most sought after queries, together with marriage/relationship.
Don't know about the Da Liu Ren system myself, but I presume Da Liu Ren covers them too.