How can one continuously generate and track several random objects with a time delay in pygame? [duplicate]

I recommend to use a timer event. Use pygame.time.set_timer() to repeatedly create an event on the event queue.
Use a pygame.sprite.Group and derive Enemy from pygame.sprite.Sprite to manage multiple enemies. Note it is important to use the attributes .image and .rect in a sprite. e.g.:

class Enemy(pygame.sprite.Sprite):
    asteroids = [pygame.image.load('rock0.png'), pygame.image.load('rock1.png'), pygame.image.load('rock2.png'),
                 pygame.image.load('rock3.png'), pygame.image.load('rock4.png')]

    def __init__(self, y, width, height):
        super().__init__() 

        self.width = width
        self.height = height
        self.vel = 1.5
        x = random.randrange(screen_width - self.width * 2)
        self.image = random.choice(self.asteroids)
        self.rect = self.image.get_rect(center = (x, y))

    def move(self):
        self.rect.y += self.vel
enemies = pygame.sprite.Group()

my_event_id = pygame.USEREVENT + 1
pygame.time.set_timer(my_event_id, 2000) # 2000 milliseconds = 2 seconds

run = True
while run:
    last = pygame.time.get_ticks()
    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            run = False

        elif event.type == my_event_id:

            # spawn new enemy
            enemies.add(Enemy(10, 64, 64))

    # [...]

    for e in enemies:
        e.move()

    # [...]

    enemies.draw(win)

If you make Projectile a pygame.sprite.Sprite, then you can use and bullets a pygame.sprite.Group, then you can use pygame.sprite.spritecollide() or pygame.sprite.groupcollide() to find hits and kill the enemies. e.g.:

class Projectile(pygame.sprite.Sprite):
    def __init__(self, x, y, width, height, color):
        super().__init__()

        self.image = pygame.Surface((width, height))
        self.image.fill(color)
        self.rect = self.image.get_rect(center = (x, y))
        self.vel = 5

    def move(self):
        self.rect.y -= self.vel

bullets = pygame.sprite.Group()

def spawn_bullet():
    if keys[pygame.K_SPACE]:
        bullets.add(Projectile((man.x + man.width // 2), (man.y - 7), 3, 7, (255, 0, 0)))
def re_draw():
    win.fill((0, 0, 0))
    enemies.draw(win)
    man.draw(win)
    bullets.draw(win)
    pygame.display.update()
while run:

    # [...]

   for e in enemies:
        e.move()
        if e.rect.y > 500:
            e.kill()
    for b in bullets:
        b.move()
        if 0 > b.rect.y or b.rect.y > 500:
            b.kill()

    pygame.sprite.groupcollide(bullets, enemies, True, True)

Full code:

import pygame
import random

pygame.init()

screen_width = 500
screen_height = 500
win = pygame.display.set_mode((screen_width, screen_height))
walk_left = [pygame.image.load('sprite_5.png'), pygame.image.load('sprite_6.png')]
walk_right = [pygame.image.load('sprite_3.png'), pygame.image.load('sprite_4.png')]
standing = [pygame.image.load('sprite_0.png'), pygame.image.load('sprite_1.png'), pygame.image.load('sprite_2.png')]


class Player:
    def __init__(self, x, y, width, height):
        self.x = x
        self.y = y
        self.width = width
        self.height = height
        self.vel = 4
        self.left = False
        self.right = False
        self.standing = True
        self.walk_count = 0
        self.hitbox = (self.x + 2, self.y + 26, 123, 45)

    def draw(self, win):
        if self.walk_count + 1 >= 12:
            self.walk_count = 0

        if not self.standing:
            if self.left:
                win.blit(walk_left[self.walk_count // 6], (self.x, self.y))
                self.walk_count += 1
            elif self.right:
                win.blit(walk_right[self.walk_count // 6], (self.x, self.y))
                self.walk_count += 1
        else:
            win.blit(standing[self.walk_count // 4], (self.x, self.y))
            self.walk_count += 1
        self.hitbox = (self.x + 2, self.y + 26, 123, 45)
        pygame.draw.rect(win, (255, 0, 0), self.hitbox, 2)


def move():
    if keys[pygame.K_LEFT] and man.x > man.vel or keys[pygame.K_a] and man.x > man.vel:
        man.x -= man.vel
        man.left = True
        man.right = False
        man.standing = False

    elif keys[pygame.K_RIGHT] and man.x < 500 - man.width - man.vel:
        man.x += man.vel
        man.left = False
        man.right = True
        man.standing = False

    else:
        man.standing = True


class Enemy(pygame.sprite.Sprite):
    asteroids = [pygame.image.load('rock0.png'), pygame.image.load('rock1.png'), pygame.image.load('rock2.png'),
                 pygame.image.load('rock3.png'), pygame.image.load('rock4.png')]

    def __init__(self, y, width, height):
        super().__init__() 

        self.width = width
        self.height = height
        self.vel = 1.5
        x = random.randrange(screen_width - self.width * 2)
        self.image = random.choice(self.asteroids)
        self.rect = self.image.get_rect(topleft = (x, y))

    def move(self):
        self.rect.y += self.vel

class Projectile(pygame.sprite.Sprite):
    def __init__(self, x, y, width, height, color):
        super().__init__()

        self.image = pygame.Surface((width, height))
        self.image.fill(color)
        self.rect = self.image.get_rect(topleft = (x, y))
        self.vel = 5

    def move(self):
        self.rect.y -= self.vel

my_event_id = pygame.USEREVENT + 1
pygame.time.set_timer(my_event_id, 2000) # 2000 milliseconds = 2 seconds


class Unit:
    def __init__(self):
        self.last = pygame.time.get_ticks()
        self.cooldown = 200

    def fire(self):
        now = pygame.time.get_ticks()
        if now - self.last >= self.cooldown:
            self.last = now
            spawn_bullet()


def spawn_bullet():
    if keys[pygame.K_SPACE]:
        bullets.add(Projectile((man.x + man.width // 2), (man.y - 7), 3, 7, (255, 0, 0)))


def re_draw():
    win.fill((0, 0, 0))
    enemies.draw(win)
    man.draw(win)
    bullets.draw(win)
    pygame.display.update()


delay = Unit()
man = Player(186, 400, 128, 128)

bullets = pygame.sprite.Group()
enemies = pygame.sprite.Group()

run = True
clock = pygame.time.Clock()
while run:
    last = pygame.time.get_ticks()
    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            run = False
        elif event.type == my_event_id:

            # spawn new enemy
            enemies.add(Enemy(10, 64, 64))

    for e in enemies:
        e.move()
        if e.rect.y > 500:
            e.kill()
    for b in bullets:
        b.move()
        if 0 > b.rect.y or b.rect.y > 500:
            b.kill()

    pygame.sprite.groupcollide(bullets, enemies, True, True)

    keys = pygame.key.get_pressed()

    move()
    delay.fire()
    clock.tick(60)
    re_draw()

pygame.quit()