namespace Class1
{
    public partial class MainWindow : Window
    {
        public TextBox getBox() { return this.textbox1; }//1. не работает

    public string TextBoxText   // 2. тоже не работает.
        {
            set { TAlert.Text = value; }
            get { return TAlert.Text; }
        }

        public MainWindow()
        {
            InitializeComponent();
        }

        public void Button_Click_1(object sender, RoutedEventArgs e)
        {
            Class2 a= new Class2(this);
        }
    }
}
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using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Class1
{
    class Class2
    {
        public MainWindow wnd;
        public System.Windows.Controls.TextBox t;

        Timer timer = new Timer(3000);

        public Class2(MainWindow win)
        {
        wnd = win;
            t = wnd.getBox();
            timer.Elapsed += new ElapsedEventHandler(OnTimedEvent);
            timer.Enabled = true;
        }
        public void OnTimedEvent(object sender, ElapsedEventArgs e)
        {
            System.Windows.Controls.TextBox t = MainWindow.getBox();
            t.Text +="Тут строки\n";
            wnd.TextBoxText += "Тут тоже не работает \n";
        }

    }
}