How do I stop more than 1 bullet firing at once?

The general approach to firing bullets is to store the positions of the bullets in a list (bullet_list). When a bullet is fired, add the bullet's starting position ([start_x, start_y]) to the list. The starting position is the position of the object (player or enemy) that fires the bullet. Use a for-loop to iterate through all the bullets in the list. Move position of each individual bullet in the loop. Remove a bullet from the list that leaves the screen (bullet_list.remove(bullet_pos)). For this reason, a copy of the list (bullet_list[:]) must be run through (see How to remove items from a list while iterating?). Use another for-loop to blit the remaining bullets on the screen:

bullet_list = []

while run == True:
    # [...]

    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            run = False

        if event.type == pygame.KEYDOWN:
            if event.key == pygame.K_SPACE:
                bullet_list.append([start_x, start_y])

    for bullet_pos in bullet_list[:]:
        bullet_pos[0] += move_bullet_x
        bullet_pos[1] += move_bullet_y
        if not screen.get_rect().colliderect(bullet_image.get_rect(center = bullet_pos))
            bullet_list.remove(bullet_pos)

    # [...]

    for bullet_pos in bullet_list[:]
        screen.blit(bullet_image, bullet_image.get_rect(center = bullet_pos))

    # [...]

See also Shoot bullet.

The states which are returned by pygame.key.get_pressed() are, set, as long a key is hold down. That is useful for the movement of a player. The player keeps moving as long a key is hold down.
But it contradicts your intention, when you want to fire a bullet. If you want to fire a bullet when a key is pressed, then can use the KEYDOWN event. The event occurs only once when a key is pressed:

while run == True:
    clock.tick(27)
    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            run = False

        if event.type == pygame.KEYDOWN:
            if event.key == pygame.K_SPACE: 
                if player1.left == True:   ## handles the direction of the bullet
                    facing = -1
                else:
                    facing = 1  
                if len(bullets) < 5:    ## max amounts of bullets on screen
                    bx, by = player1.x + player1.width //2 ,player1.y + player1.height//2
                    bullets.append(projectile(bx, by, 6, black, facing))

    # [...]

If you want to implement some kind of rapid fire, then the things get more tricky. If you would use the state of pygame.key.get_pressed() then you would spawn one bullet in every frame. That is far too fast. You have to implement some timeout.
When a bullet is fired, the get the current time by pygame.time.get_ticks(). Define a number of milliseconds for the delay between to bullets. Add the dela to the time and state the time in a variable (next_bullet_threshold). Skip bullets, as long the time is not exceeded:

next_bullet_threshold = 0

run = True
while run == True:

    # [...]

    current_time = pygame.time.get_ticks()
    if keys[pygame.K_SPACE] and current_time > next_bullet_threshold:

        bullet_delay = 500 # 500 milliseconds (0.5 seconds)
        next_bullet_threshold = current_time + bullet_delay

        if player1.left == True:   ## handles the direction of the bullet
            facing = -1
        else:
            facing = 1  
        if len(bullets) < 5:
            bx, by = player1.x + player1.width //2 ,player1.y + player1.height//2
            bullets.append(projectile(bx, by, 6, black, facing))

Minimal example: repl.it/@Rabbid76/PyGame-ShootBullet

import pygame
pygame.init()

window = pygame.display.set_mode((500, 200))
clock = pygame.time.Clock()

tank_surf = pygame.Surface((60, 40), pygame.SRCALPHA)
pygame.draw.rect(tank_surf, (0, 96, 0), (0, 00, 50, 40))
pygame.draw.rect(tank_surf, (0, 128, 0), (10, 10, 30, 20))
pygame.draw.rect(tank_surf, (32, 32, 96), (20, 16, 40, 8))
tank_rect = tank_surf.get_rect(midleft = (20, window.get_height() // 2))

bullet_surf = pygame.Surface((10, 10), pygame.SRCALPHA)
pygame.draw.circle(bullet_surf, (64, 64, 62), bullet_surf.get_rect().center, bullet_surf.get_width() // 2)
bullet_list = []
max_bullets = 4
next_bullet_time = 0
bullet_delta_time = 200 # milliseconds

run = True
while run:
    clock.tick(60)
    current_time = pygame.time.get_ticks()
    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            run = False

        if event.type == pygame.KEYDOWN:
            if len(bullet_list) < max_bullets and current_time >= next_bullet_time:
                next_bullet_time = current_time + bullet_delta_time
                bullet_list.insert(0, tank_rect.midright)

    for i, bullet_pos in enumerate(bullet_list):
        bullet_list[i] = bullet_pos[0] + 5, bullet_pos[1]
        if bullet_surf.get_rect(center = bullet_pos).left > window.get_width():
            del bullet_list[i:]
            break

    window.fill((224, 192, 160))
    window.blit(tank_surf, tank_rect)
    for bullet_pos in bullet_list:
        window.blit(bullet_surf, bullet_surf.get_rect(center = bullet_pos))
    pygame.display.flip()

pygame.quit()
exit()