Does sharing installed apps pose a risk of sharing personal data? Let's say I install an app on my phone from the play store. Now I want to give this app to a friend. I use an app called File Commander to share an installed app via bluetooth.  

Will any settings or data used in my app also be sent with the apk, or just the app itself?

Thank you.
Most likely, it is not going to send the app data with the app.

If the only file being sent is an apk (example: angrybirds.apk), then there is no data sent with it. The apk is just the app itself.

However it is possible to send app data. If you are using "File Commander", it would depend on whether File Commander sends app data or not (sorry I don't have this app). It may be an option in the settings, so you could perhaps enable/disable the sending of data along with the app.