Using Multithreading with Async-await C#

Ok, feel free to ignore all the changes I've made but I couldn't help but modify the way some of the variables read and the code looked. This is not a working application and I have obviously not tested it. This is just a cleaned up version of what you have with a suggested way of using Task. It's also mocked using just the code you've provided so it is what it is. #2 is, what I believe, the answer you needed.

1. In Main I removed the words 'thread' since that's not actually what's happening. It may be, but we don't know if the HttpClient is indeed starting a new thread or just holding / returning from the rest call. Using async / await does not always mean a Thread was started (although it's common to think of it that way).
2. I used .Result (not Wait() as I suggested in comments) to get the result of the task. This is ok since it's a console app but not ideal for a real world app that needs to operate without blocking. I also removed Task.WaitAll with this change.
3. I renamed functions to have verbage because, IMO, functions should be doing work and the naming should describe the work being done.
4. I renamed some variables because, IMO, variables should be PascalCase when their scope isn't in a method or private and camelCase when they are. The names should also, IMO, be what it is followed by the Type that makes sense.
5. I appended 'Async' to function names that return a running Task.
6. Changed FacebookClient to be singleton and allowing only one HttpClient to be used instead of many and allowing it to be disposed; plus more.
7. Added alternate version of the GetFacebookData function that calls the tasks and awaits them all simultaneously.

static void Main(string[] args)
{
    string[] dataSet = new string[] { /* mocked */ };  // [ids_group]; <- no idea what this is so I mocked it.

    for (int i = 0; i < dataSet.Length; i++)
    {
        Console.WriteLine("Main... " + (i + 1).ToString());
        var result = GetFacebookData(dataSet[i]);
        WriteToTxt(result);
        Console.WriteLine("Complete... " + (i + 1).ToString());
        //do sth
    }

    Console.Read();
}

private static Dictionary<string, string[]> GetFacebookData(string idsString)
{
    var allDataDictionary = new Dictionary<string, string[]>();
    var idsArray = idsString.Split(',');

    foreach (var id in idsArray)
    {
        var response = FacebookClient.Instance.GetDataAsync<string[]>(id).Result;
        allDataDictionary.Add(id, response);
    }

    return allDataDictionary;
}

public class FacebookClient
{
    private readonly HttpClient httpClient;
    private readonly string facebookApiVersion;
    private readonly string accessToken;

    public static FacebookClient Instance { get; } = new FacebookClient();

    FacebookClient()
    {
        facebookApiVersion = ConfigurationManager.AppSettings["fb_ver"];
        accessToken = ConfigurationManager.AppSettings["accessToken"];

        httpClient = new HttpClient
        {
            BaseAddress = new Uri("https://graph.facebook.com/" + facebookApiVersion + "/"),
            Timeout = TimeSpan.FromSeconds(15)
        };

        httpClient.DefaultRequestHeaders.Accept.Add(new MediaTypeWithQualityHeaderValue("application/json"));
    }

    public async Task<T> GetDataAsync<T>(string facebookId)
    {
        var response = await httpClient.GetAsync($"{facebookId}?access_token={accessToken}");
        if (!response.IsSuccessStatusCode) return default;
        var result = await response.Content.ReadAsStringAsync();
        return JsonConvert.DeserializeObject<T>(result);
    }

    ~FacebookClient() => httpClient.Dispose();
}

Here's a version that's starting all the tasks and then awaiting them all at the same time. I believe this might give you some issues on the HttpClient but we'll see.

private static Dictionary<string, string[]> GetFacebookData(string idsString)
{
    var allDataDictionary = new Dictionary<string, string[]>();
    var idsArray = idsString.Split(',');
    var getDataTasks = new List<Task<string[]>>();

    foreach (var id in idsArray)
    {
        getDataTasks.Add(FacebookClient.Instance.GetDataAsync<string[]>(id));         
    }

    var tasksArray = getDataTasks.ToArray();
    Task.WaitAll(tasksArray);
    var resultsArray = tasksArray.Select(task => task.Result).ToArray();

    for (var i = 0; i < idsArray.Length; i++)
    {
        allDataDictionary.Add(idsArray[i], resultsArray[i]);
    }

    return allDataDictionary;
}