Hey Synycalwon, I think I can help you out a little bit. (Just a side ramble, but as developers we're actually really disappointed with how Google "simplified" their permissions. They grouped a lot of stuff together that makes it really hard for consumers to really understand what permissions the app actually has.)
If I remember correctly, the first permission was necessary because we are running a background activity that actually executes separately from the main activity that is responsible for displaying the Live Notification mode and gathering logs for user. Of course, the app needs to check to be sure additional background activities are not spawned unnecessarily.
The next two you listed were added because of our user requests, which we take really seriously. The app absolutely monitors to check if you are on a call or not! The reason being because many of our users, many being wireless engineers, run one of the discover modes of the application that continuously refreshes the connection. If the user receives a call during one of these cycles then the app pauses that so that it won't end up kicking a user off the call by refreshing the connection. Run at start up was a popular request that we actually just implemented. I personally never really saw the need for it, but we probably got at least fifteen emails a week from users asking for it. Since we added it I've actually found it really useful. (Disabled by default in the settings).
The in-app purchase is really a feature that helps us out a lot. Really helps cut down on piracy which is a huge problem for us since our gains are very small compared to amount of time we devote to the app. A lot of people might not realize it but we have actually accumulated thousands of man hours into the application. My partner, Dan, works exclusively on the app almost all day everyday and I spend any time I am not working on my graduate projects working on the app. A break from grad school for me usually means an 80 hour week that goes into the app. So the in-app purchases just help us protect the small returns the app generates for us. You're never charged for something without you knowing and we refund nearly all the users who email us and say that they somehow "accidentally" bought the app.
Any other permissions you may be interested in? I am going to be working on projects for the rest of the night and am presenting at an engineering symposium tomorrow, but I could get back to you tomorrow evening. Or if you email the feedback email address for us Dan could respond to you pretty quickly in the morning.
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