In general terms about the Dart language

import 'package:flutter/material.dart';

void main() => runApp(MyApp());

class MyApp extends StatefulWidget {
  @override
  _MyAppState createState() => _MyAppState();
}

class _MyAppState extends State<MyApp> {
  int _counter = 0;

  void _incrementCounter() {
    setState(() {
      _counter++;
    });
  }

  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      home: Scaffold(
        appBar: AppBar(
          title: Text('Пример StatefulWidget'),
        ),
        body: Center(
          child: Column(
            mainAxisAlignment: MainAxisAlignment.center,
            children: <Widget>[
              Text('Вы нажали на кнопку столько раз:'),
              Text('$_counter', style: Theme.of(context).textTheme.headline4),
            ],
          ),
        ),
        floatingActionButton: FloatingActionButton(
          onPressed: _incrementCounter,
          tooltip: 'Increment',
          child: Icon(Icons.add),
        ),
      ),
    );
  }
}

Flutter makes it easier to work with asynchronous operations by using FutureBuilder:

import 'package:flutter/material.dart';
import 'dart:async';

void main() => runApp(MyApp());

class MyApp extends StatelessWidget {
  final Future<String> _calculation = Future<String>.delayed(
    Duration(seconds: 2),
    () => 'Данные загружены',
  );

  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      home: Scaffold(
        appBar: AppBar(
          title: Text('Пример FutureBuilder'),
        ),
        body: Center(
          child: FutureBuilder<String>(
            future: _calculation,
            builder: (BuildContext context, AsyncSnapshot<String> snapshot) {
              List<Widget> children;

              if (snapshot.connectionState == ConnectionState.done) {
                if (snapshot.hasError) {
                  children = <Widget>[
                    Icon(
                      Icons.error_outline,
                      color: Colors.red,
                      size: 60,
                    ),
                    Padding(
                      padding: const EdgeInsets.only(top: 16),
                      child: Text('Error: ${snapshot.error}'),
                    ),
                  ];
                } else {
                  children = <Widget>[
                    Icon(
                      Icons.check_circle_outline,
                      color: Colors.green,
                      size: 60,
                    ),
                    Padding(
                      padding: const EdgeInsets.only(top: 16),
                      child: Text('Result: ${snapshot.data}'),
                    ),
                  ];
                }
              } else {
                children = <Widget>[
                  SizedBox(
                    child: CircularProgressIndicator(),
                    width: 60,
                    height: 60,
                  ),
                  const Padding(
                    padding: EdgeInsets.only(top: 16),
                    child: Text('Awaiting result...'),
                  )
                ];
              }

              return Column(
                mainAxisAlignment: MainAxisAlignment.center,
                crossAxisAlignment: CrossAxisAlignment.center,
                children: children,
              );
            },
          ),
        ),
      ),
    );
  }
}

Passing data between screens is usually done through constructors and the Navigator API:

import 'package:flutter/material.dart';

void main() => runApp(MyApp());

class MyApp extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      title: 'Передача данных между экранами',
      home: FirstScreen(),
    );
  }
}

class FirstScreen extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        title: Text('Первый экран'),
      ),
      body: Center(
        child: ElevatedButton(
          child: Text('Перейти ко второму экрану'),
          onPressed: () {
            Navigator.push(
              context,
              MaterialPageRoute(
                builder: (context) => SecondScreen(data: 'Привет от первого экрана'),
              ),
            );
          },
        ),
      ),
    );
  }
}

class SecondScreen extends StatelessWidget {
  final String data;

  SecondScreen({Key key, @required this.data}) : super(key: key);

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        title: Text('Второй экран'),
      ),
      body: Center(
        child: Text(data),
      ),
    );
  }
}

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