How to have an individual notification for every message? Similar to the iPhone, is there any way I can get a separate, individual notification for every SMS, update, (any sort of notification)? 

This is not specific to SMS, but rather to any app.

Currently, my phone will chunk notifications by the app and once I get 5+ notifications from an individual app, my phone will chunk the notifications together and I can no longer see the notifications unless I deliberately click on the notifications.
Customising android to mimic ios notification style

While android os is still lagging behind ios in terms of personalisation and notfications there are a dozen of applications
that come close to mimicking this behaviour, in my research I managed to grab just a few:




Defumblr Smart Lock


     

Key Features:


Defumblr highlights your important messages in a unified messaging interface
Launch your most used apps with Quick App Launcher
Sync the Lock screen Calendar and Alarm with your Android system.
Organize critical to-do items right on your lock screen with a customized To-Do List widget
Get glanceable forecasts with the Weather widget
Organize all your important notifications and messages in one place
Personalized configuration options including layout, color schemes and backgrounds
Secure your phone with password or PIN protection
Customize which apps to feature on your lock screen





AcDisplay 


AcDisplay 
 is a good example that completely replicates Apple’s functionality.


  It uses the sensors on your device to know when to wake up, saving you
  from hitting the home button or power button on your device.  It’s
  also customisable, so you can adjust which notifications you want to
  show up, plus use some power saving settings and dynamic backgrounds.


Screenshots:






SlideLock 



  is a simple and clean locker with powerful notification features.


Features :


Simple and clean android locker replacement
Swipe the screen to the right to unlock, swipe it to the left to access the camera
Actionable detailed notifications, double tap to open, swipe to dismiss
PIN and pattern security
Screen wakes up for a short time when receiving a notification, allowing you to perform a quick check without having to touch the device
Custom settings for each app (sound, vibration, ...)
Notification banners when your device is unlocked
Low battery usage


Screenshots:

   

Hope this helps