These are really broad questions, hence difficult to answer in a helpful way.
When writing a research plan/statement when applying for an assistant professor position, how should be the document structured?
If the application guidance gives no details, it's entirely up to you to decide on that. Have you approached the contacts where you are applying to ask them directly? If that matters to you that much, you should not mind asking for additional details.
Should these be general topics or as specific as a research proposal?
Again, it's entirely up to you to decide on that. Think also in terms of disciplinary habits. Are proposals in your discipline rather generic or thorough?
Should I prove that I have a strong background in these fields or it is enough that the ideas are novel and attractive?
Think if you were in a position to select applicants: what would you prefer? Probably a combination of both. If someone has little experience in a field, probability to come up with novel and attractive is smaller, I would think, don't you?
Should I include technical data/figures or the purpose is just the general description?
If you feel like technical data is needed and useful to make your line of argument and your whole proposal stronger and more compelling in order to be selected, why not go for it?
Should I explain expected outcome as we do in a proposal?
If you are used to explain expected research outcomes in your field of expertise, why do any different this time? Recruiting colleagues are bound to appreciate a clear and long-sighted research proposal and vision.