Rich Text box scroll to the bottom when new data is written to it

Yes, you can use the ScrollToCaret() method:

// bind this method to its TextChanged event handler:
// richTextBox.TextChanged += richTextBox_TextChanged;
private void richTextBox_TextChanged(object sender, EventArgs e) {
   // set the current caret position to the end
   richTextBox.SelectionStart = richTextBox.Text.Length;
   // scroll it automatically
   richTextBox.ScrollToCaret();
}