My facebook account is causing my mobile phone to run slow and it keeps restarting. Is it safe to force stop facebook?
First, it's not your account that is slowing down your smart phone, it's the app itself (don't worry, even I had the same problem).
Your phone is probably weak or you are running too much of apps and processes at the same time, saving less resources for facebook.
So, to answer your qustion: No, your account will not be deleted if you force stop facebook (or any other app like google+). Deleting an account is a totaly different process. For that you will have to request facebook to delete your account. But what's hapening in your case is simply stopping the app (for geeks: the front end part) from doing further work. Your account detailes and stuff are perfectly safe at facebook's server (for geeks: back end).
So go ahead, force stop your app. You can still use facebook from their mobile site, which is not heavy and much resource consuming.
Happy facebooking =)