profile_pic.cs

using UnityEngine;
using System.Collections;
using System.Collections.Generic;
using Facebook.Unity;
using UnityEngine.UI;

public class fb_api : MonoBehaviour {

    public Button showProfilePic;
    public Image profilePic;

    void Awake ()
    {
        if (!FB.IsInitialized) {
            // Initialize the Facebook SDK
            FB.Init(InitCallback, OnHideUnity);
        } else {
            // Already initialized, signal an app activation App Event
            FB.ActivateApp();
        }
    }

    void Start()
    {
        StartCoroutine(loginAfter());

        showProfilePic.onClick.AddListener(getProfilePic);
    }

    // methods to login and retrieve profile pic
    IEnumerator loginAfter()
    {
        yield return new WaitForSeconds(0.5f);
        LoginFB();
    }
    
    private void LoginFB()
    {
        var perms = new List<string>(){"public_profile", "email", "user_friends"};
        FB.LogInWithReadPermissions(perms, AuthCallback);
    }

    void getProfilePic()
    {
        FB.API("/me/picture", HttpMethod.GET, ProfilePhotoCallback);
    }

    // Facebook class methods
    private void InitCallback ()
    {
        if (FB.IsInitialized) {
            // Signal an app activation App Event
            FB.ActivateApp();
            // Continue with Facebook SDK
            // ...
        } else {
            Debug.Log("Failed to Initialize the Facebook SDK");
        }
    }

    private void OnHideUnity (bool isGameShown)
    {
        if (!isGameShown) {
            // Pause the game - we will need to hide
            Time.timeScale = 0;
        } else {
            // Resume the game - we're getting focus again
            Time.timeScale = 1;
        }
    }
    
    private void AuthCallback (ILoginResult result) {
        if (FB.IsLoggedIn) {
            // AccessToken class will have session details
            var aToken = Facebook.Unity.AccessToken.CurrentAccessToken;
            // Print current access token's User ID
            Debug.Log(aToken.UserId);
            // Print current access token's granted permissions
            foreach (string perm in aToken.Permissions) {
                Debug.Log(perm);
            }
        } else {
            Debug.Log("User cancelled login");
        }
    }

    private void ProfilePhotoCallback(IGraphResult result)
    {
        if (string.IsNullOrEmpty(result.Error) && result.Texture != null)
        {
            Sprite p = Sprite.Create(result.Texture, new Rect(0,0,result.Texture.width, result.Texture.height), new Vector2(0.5f, 0.5f));
            profilePic.sprite = p;
        }
    }
}

unity_facebook.cs

using UnityEngine;
using System.Collections;
using System.Collections.Generic;
using Facebook.Unity;
using UnityEngine.UI;
using Facebook.MiniJSON;

public class profile : MonoBehaviour 
{
    public GameObject fbname;
    public GameObject fbava;
    private Dictionary<string, string> aaa = null;
    
    private void DealWithProfilePicture(IGraphResult result)
    {
        if (result.Error != null) 
        {
            Debug.Log ("problem with getting profile");
            FB.API(Util.GetPictureURL("me", 128, 128), HttpMethod.GET, DealWithProfilePicture);
            return;
        }
        
        Image UserAvatar = fbava.GetComponent<Image> ();
        UserAvatar.sprite = Sprite.Create (result.Texture, new Rect (0, 0, 128, 128), new Vector2 (0, 0));
    }
    
    private void DealWithUsername(IGraphResult result)
    {
        if (result.Error != null)
        {
            Debug.Log ("problem with getting username");
            FB.API ("/me?filed=id,first_name", HttpMethod.GET, DealWithUsername);
            return;
        }
        
        aaa = Util.DeserializeJSONProfile(result.RawResult);
        Text Username = fbname.GetComponent<Text> ();
        Username.text = "Hello, " + aaa["first_name"];
    }
}