Hey Jan,
Sorry for the delay on getting back to you. Answers below.
Put my name on the "HSR-list"! I want to have this setting, too. 
I would also appreciate to have the option to select the external settings of my shock and let the Shockwiz focus on these settings. I think this would improve the usability a lot, and maybe also the overall result of the optimization.
In respects to HSR, consider your name added. As for the settings selector, that may or may be something that appears. Unfortunately it may not be as easy as just hiding them. If you simply hide them from view, their impact on your Shock Tuning Score will still apply. You may end up in a situation where all the 'visible' Suggestions indicate 'OK' but but a 'hidden' adjustment is asking for change keeping you from that elusive Shock Tuning Score of 100. Hiding that from view would only create confusion. So at this point, including them and having the user ignore what they can't change, is no different than simply hiding them.
I'm thinking about a situation where the app tells me to change HSC, but if I run a Pike, I can't change that. So I will try to change something else, and maybe the app will tell me again to change the HSC. I think, if you limit the degree of freedom of the algorithm to what's actually possible, you might get a better result in the end that compensates the settings you can't change on your individual shock/fork.
I see what you're saying, but at the end of the day you're not likely to end up in a different spot. If you do find yourself in a situation where everything but HSC indicates "OK", changing your Baseline Air Pressure (or which ever adjustment you choose) probably isn't going to correct it. Or worse, making an adjustment in an attempt to correct HSC will throw something more important out of balance. Remember that just because HSC on a Pike is not externally adjustable does not mean it does not have HSC. Isn't it better to know how that internal tune is working? In the end we feel that it is.
Maybe you could also provide two different recommendations/modes in the app, one only with external settings, and for the advanced users, one that also includes settings that must be change by internal modifications of the damper system.
That's not a bad idea except ShockWiz is designed to be brand agnostic. And even if it were tailored to a specific brand, not all models within one brand have the same dials as the rest.
1. If I have optimized my suspension with one of the tuning styles and am not satisfied with it and want to try out another, will the app directly tell me how to change my settings (at least a rough direction)? Or do I have to start all over again?
So, if we're talking about a single ride session then you don't have to start over. Changing the Tuning Style can be done at anytime and will not erase existing ride data. All existing data will recalculate to the new style which provides a new Shock Tuning Score, Suggestions and Detections. However, as soon as you select 'Start New Session' (which should be done after acting on any one Suggestion) this data is erased. So, if your talking about multiple ride sessions you have to start over, sort of.
ShockWiz works by directing us to a place that we like to call the 'Window of Happiness'. As the name suggest (window) it's not trying to direct us to a single point. The Window of Happiness consists of an acceptable range that we can be within. All four Tuning Styles exist within this window. Then, each individual tuning style occupies it's own portion of that window. So even if you tune to a particular Tuning Style and want to switch, you won't have that far to go. You're already within the larger window and just need to shuffle from side to the other.
Quote from your tutorial: "You can always pick and choose what you like from each Tuning Style. Eg: Tune the Baseline pressure and ramp from one Tuning Style and then switch Tuning Styles to tune the dampers."
What is the actual benefit of doing that? Can you make an example? This sounds a little bit complicated and might mess up the overall setup if you are not knowing what you are doing.
This is certainly a more advanced way to use ShockWiz and will not apply to most. The benefit in doing this is to simply offer greater customization.
Each tuning style has it's own set of parameters, or window, that it deems acceptable for every adjustment. Because of this, each Tuning Style will offer it's own unique tune and ride characteristics. Picking and choosing certain parts of multiple Tuning Styles just makes it that much more granular.
If you have your bike tuned to Balanced and enjoy how it feels, but think the spring is still a bit too soft for you liking, follow the Suggestion for Baseline Air Pressure and Air Spring Ramp under 'Efficient' to firm it up.
Or you really like how the bike feels in Balanced but feel the rebound is a bit to sluggish, follow the Suggestion for Rebound within Playful, the parameters set allow it to be a bit faster.
Again this will not apply to most, and in fact I don't even do this myself, just know it's possible.
Can you give a little more technical explanation about the different tuning styles? What is the criteria the suspension is being optimized to? Will it be basically LSC to reduce pedal influence or is there more to it? This is the first decision I have to make and I can't really decide if Playful or Aggressive would be best for me.
The app has information baked in that offers a quick explanation of this. We also have an article here that addresses it in more detail,
here.
At the end of the day you might be thinking about this too much. If you buy a device the best thing to do is experiment a bit until you find what's right. Plus it's very easy to adjust the bike from one style to another once you're within the window.
Remember that there are certainly very WRONG ways to setup suspension but no 'perfect' ways. Once you're within the 'Window of Happiness' you can start experimenting with slightly increasing and decreasing certain adjustments to fine tune how the bike feels.
I usually suffer from arm pump and pain in the fingers very fast, so I should maybe choose Aggressive to have the best bump compliance. But I also like to have a bike that "feels light" and can be lifted good over small jumps. I also need more "safety" when going over kickers/jumps to get a good position in the air. For that, I think Playful could be better. It would be nice to have some more details about that.
PS: I'm running a 160 mm Enduro/AM with a 180 mm fork.
Balanced is a very good place to start. I would suggest starting here and tune your bike in the order prescribe
here. From there you can change the tuning style and see what effect it has.
Doing some hand and forearm strengthening exercises won't hurt either!
Alex@Quarq