Permissions required for using an app for a study What kind of permissions do I need to obtain from the developer of an app if I am planning to use it in a study? 
The study primarily aims to look at how different students learn mobile games differently, and what factors determines their score.

Since it is relevant to the study, we would also have to analyse the game itself, quantify how the difficulty evolves over time, and what amount of randomness is involved in each gameplay (to get somehing like a stochastic index).


So, in case this ever goes to publication, would mentioning the app-name be necessary, since its characterisation would already be a part of it?
Do we need to obtain permission before even using it, since it is already a free app in the play store? Doesn't its free status give us permission to use it in a study (at least an unpublished one)?


There are no commercial interests in either of the cases. I am not sure if it is okay to mention the name here too. Sorry if I seem to be over-thinking but I am new to the world of academia! Any guidance is appreciated. (Unsure of the tags too)
Yes, of course you should mention the name of the app. You have to provide details of your methodology. You should also cite the app (I see this commonly done by citing the app store page for it, but maybe your field has a different convention).
I have never heard of a researcher obtaining permission to run a study involving particular software. I have led or collaborated on about ten human-subjects studies involving a variety of free and commercial software.