First, remember that casing isn't just about memorizing every step, industry, case type, etc. It's about learning how to be adaptable and nimble. So, always be prepared for the unexpected.
1. All cases are structured, wheather you realise the structure or not. It's your job to keep it organised and keep it to a good flow/framework!
2. Figure out what data/information you need and ask for it: The interviewer won't just give it to you (just like your client won't know what you need from them). Use your framework to dive into areas! If your interviewer insists they don't have data in that area (after you've gone specific), then go into another area of your framework (or expand out).
3.In this case try and keep a mini framework in your head. You can write as you talk as well.
When you say "not those kinds of questions an interview-led style would ask" this shows me that you're limited in your preparation....don't come in expecting a certain format/style! Be ready to drive your own case if needed. Think if you were on a real life project and asked to lead it...this is what they need you to demonstrate!
Honestly, I think you could benefit from a session with a coach. Finding other PrepLoungers to case with is great to get you 80% of the way there, but coaches will really test your thinking and make sure you truly understand what you're saying/doing. Intimately understanding the case/situation/problem and knowing why you're asking x question is the key to being able to adapt to whatever you encounter during the interview.