I got ideas from this tutorial: Python Snake Game

using System;
using System.Collections.Generic;
using System.Drawing;
using System.Windows.Forms;

namespace Snake
{
    public partial class Form1 : Form
    {
        // Snake list of (x, y) positions
        private List<Point> _snake = new List<Point>()
        {
            new Point(10, 10)
        };

        // Snake movement direction
        private Point _snakeDir = new Point(10, 0);

        // Food
        private Point _food = new Point();

        // Random generator
        private Random _rnd = new Random();

        // Game field size
        private int _fieldWidth = 200;
        private int _fieldHeight = 200;

        // Snake step
        private int _snakeStep = 10;

        public Form1()
        {
            InitializeComponent();

            // Centers the form on the current screen
            CenterToScreen();

            // Set a game field size
            ClientSize = new Size(_fieldWidth, _fieldHeight);

            // Generate an initial random position for the food
            GenerateFood();

            // Create a timer for the GameLoop method
            var timer = new Timer();
            timer.Tick += GameLoop;
            timer.Interval = 200;
            timer.Start();
        }

        private void Form1_Paint(object sender, PaintEventArgs e)
        {
            Draw();
        }

        private void GameLoop(object sender, System.EventArgs e)
        {
            Update();
            Invalidate();
        }

        private void Update()
        {
            // Calc a new position of the head
            Point newHeadPosition = new Point(
                _snake[0].X + _snakeDir.X,
                _snake[0].Y + _snakeDir.Y
            );

            // Insert new position in the beginning of the snake list
            _snake.Insert(0, newHeadPosition);

            // Remove the last element
            _snake.RemoveAt(_snake.Count - 1);

            // Check collision with the food
            if (_snake[0].X == _food.X &&
                _snake[0].Y == _food.Y)
            {
                // Add new element in the snake
                _snake.Add(new Point(_food.X, _food.Y));

                // Generate a new food position
                GenerateFood();
            }
        }

        private void Draw()
        {
            DrawFood();
            DrawSnake();
        }

        private void DrawSnake()
        {
            foreach (var cell in _snake)
            {
                DrawRect(cell.X, cell.Y, Color.Green);
            }
        }

        private void DrawFood()
        {
            DrawRect(_food.X, _food.Y, Color.OrangeRed);
        }

        private void DrawRect(int x, int y, Color color, int size = 10)
        {
            Graphics g = CreateGraphics();
            SolidBrush brush = new SolidBrush(color);
            g.FillRectangle(brush, new Rectangle(x, y, size, size));
            brush.Dispose();
            g.Dispose();
        }

        private void GenerateFood()
        {
            _food.X = 10 * _rnd.Next(0, _fieldHeight / 10 - 1);
            _food.Y = 10 * _rnd.Next(0, _fieldHeight / 10 - 1);
        }

        private void Form1_KeyPress(object sender, KeyPressEventArgs e)
        {
            switch (e.KeyChar)
            {
                case 'w':
                    _snakeDir.X = 0;
                    _snakeDir.Y = -_snakeStep;
                    break;
                case 'a':
                    _snakeDir.X = -_snakeStep;
                    _snakeDir.Y = 0;
                    break;
                case 's':
                    _snakeDir.X = 0;
                    _snakeDir.Y = _snakeStep;
                    break;
                case 'd':
                    _snakeDir.X = _snakeStep;
                    _snakeDir.Y = 0;
                    break;
            }
        }
    }
}

I will look at your code and see how I can use it in my game.