public static HttpClientHandler httpClientHandler = new HttpClientHandler()
private static HttpClient Client = new HttpClient(handler: httpClientHandler, disposeHandler: true) { MaxResponseContentBufferSize = 10000000 };

private Button1_Click(Object sender, EventArgs e)
{
    httpClientHandler.Proxy = null;
    httpClientHandler.UseProxy = false;
    await DoWork();
}

public async Task DoWork()
{
    var allTasks = new List<Task>();
    for (int i = 0; i < dt.Rows.Count; i++)
    {
        if(Some condition)
        allTasks.Add(Task.Run(() => GetApiData()));
    }
    Task waitAll = Task.WhenAll(allTasks);
    await waitAll;
}

public async Task GetApiData()
{
    var Result= await (await Client.GetAsync("Some Url")).Content.ReadAsStringAsync();
    //do some cpu bound(but not too heavy, like search in a datatable that have 20 rows) work on Result.
}