How to detect collisions between two rectangular objects or images in pygame

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Use pygame.Rect objects and colliderect() to detect the collision between the bounding rectangles of 2 objects or 2 images:

rect1 = pygame.Rect(x1, y1, w1, h1)
rect2 = pygame.Rect(x2, y2, w2, h2)
if rect1.colliderect(rect2):
    # [...]

If you have to images (pygame.Surface objects), the bounding rectangle of can be get by get_rect(), where the location of the Surface has to be set by an keyword argument, since the returned rectangle always starts at (0, 0):
(see Why is my collision test not working and why is the position of the rectangle of the image always wrong (0, 0)?)

def game_loop():
    # [...]

    while running:
        # [...]

        player_rect = player_img.get_rect(topleft = (x, y))
        for i in range(len(things_cor)):
            thing_rect = things_added[i].get_rect(topleft = things_cor[i])

            if player_rect.colliderect(thing_rect):
                print("hit")

        player(x, y)
        x += x_change

        for i in range(len(things_cor)):
            thing_x, thing_y = things_cor[i]
            things(thing_x, thing_y, things_added[i])

Use pygame.time.get_ticks() to delay the start of the game for a certain time. pygame.time.get_ticks() return the number of milliseconds since pygame.init() was called. For instance:

def game_loop():
    # [...]

    while running:
        passed_time = pygame.time.get_ticks() # passed time in milliseconds
        start_time = 100 * 1000 # start time in milliseconds (100 seconds)
        
        # [...]

        # move player    
        if passed_time >= start_time:
            x += x_change
            if x < 0:
                x = 0
            elif x > display_width - player_width:
                x = display_width - player_width
    
        # move things
        if passed_time >= start_time:
            for i in range(len(things_cor)):
                things_cor[i][1] += y_change
                if things_cor[i][1] > display_height:
                    things_cor[i][1] = random.randint(-2000, -1000)
                    things_cor[i][0] = random.randint(0, display_width)
                    things_added[i] = random.choice(thing_imgs)

                    things_added.append(random.choice(thing_imgs))

                    if len(things_added) < 6:
                        things_cor.append(
                            [random.randint(0, display_width), -10])

        # draw scene and update dispaly
        game_display.fill(white)
        player(x, y)
        for i in range(len(things_cor)):
            thing_x, thing_y = things_cor[i]
            things(thing_x, thing_y, things_added[i])
        pygame.display.update()
        clock.tick(60)

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