MMRemote asks for permission to read the phone state in order to pause your music/mute/lower your volume when you receive a phone call. You can choose which of these actions you want (or no action) in the Settings. MMRemote will not use your phone state for anything else, and will not read any other phone related information (such as your phone number, or your contacts).
MMRemote asks for permission to access the internet. This permission is required for any network activity, and must be allowed for the remote to work, since the remote uses your network to communicate with your computer (none of the regular traffic goes out to the internet). In addition, MMRemote also communicates with mmremote.net when (if) you use connection strings, and to send error reports and simple usage statistics.
If you send a crash/bug report, the report will be securely transmitted to Google Crashlytics, which is the solution I use to handle crash/bug reports. These reports contains the phone model your are using, the Android version that is installed, and information about the code that caused the crash, so that I can find and fix the bug. In addition to crash reports, Crashlytics also collects anonymous usage statistics, so that I can see how many people are using the app, and to a certain degree which features are most popular. No identifying information is collected in any of these reports, and nothing will be seen by anybody else than me.
In general, MMRemote collects no private data from your device. [For MMRemote4 only:] If you have made a donation using a non-Google Play e-mail, that e-mail is stored in a secure database in order to let you activate the bonus features from the app.