Client-side, then() or other?

Question 1

I think you want to do something like this, but I don't yet fully understand what you try to accomplish. Can you please just add a comment what you need differently?

Map data;

void main() {
  //(querySelector('[name="push"]') as ButtonInputElement).onClick.listen(btnClickHandler);
  (querySelector('[name="push"]') as ButtonInputElement).onClick.first.then(btnClickHandler);

  // this would work too, because every element has the click event.
  // querySelector('[name="push"]').onClick.listen(btnClickHandler);
}

void btnClickHandler(MouseEvent e) {
  String name = (querySelector('[name="pseudo"]') as TextInputElement).value;    

  data = {'pseudo': name}; 
  String encode = JSON.encode(data);

  WebSocket wss = new WebSocket('ws://127.0.0.1:4040/ws');
  wss.onOpen.listen((_) => wss.send(encode));
  wss.onMessage.listen((msg) => print("Msg received : ${msg.data}"));
}

Question 2

For such a simple use case you can do it this way

Future<String> ft_get_pseudo()
{
  return new Future(() {
    InputElement button;
    InputElement text;

    text = querySelector('[name="pseudo"]');
    button = querySelector('[name="push"]');
    button.onClick.listen((_) => _completer.complete(text.value));
  }
}

Question 3

If I understand you correctly, you want to get text.value from the ft_get_pseudo() function when you push on the button, right? If so, you need to create a new Completer and return its Future at the end of the ft_get_pseudo(). Then, in the button's onClick event, you just complete the future with the value of text.value.

Code might be something like this:

Future<String> ft_get_pseudo()
{
  Completer _completer = new Completer();

  InputElement button;
  InputElement text;

  text = querySelector('[name="pseudo"]');
  button = querySelector('[name="push"]');
  button.onClick.listen((_) => _completer.complete(text.value));

  return _completer.future;
}