I am hoping to configure my SUITECRM such that anybody attached to a case can also get an email notification just as the person who opened the case gets an sms notification. Is this achieveable? If yes, how do I go about it.
What do you mean about the SMS notification? Is this some add-on that you’re using, or are you just expressing a feature that you also wish you had?
You can make some customizations to send out additional email notifications when some action happens, but when exactly do you want this to happen? When some specific field changes? Like Status, perhaps? Or some other action related to the Case? Which ones?
Maybe this can be achieved with a Workflow, or for more power and control you can use some PHP code in a logic hook.
I have this add-on that sends SMS notifications to anyone that opens a case. During the process of opening a case, they are required to fill their phone number with which they will receive the notification about the status. So I also want the person attached to the mail to also get notification once the case is opened and when the case status changes.
Have you tried a Workflow reacting to the status change and sending Emails?
I am not sure you can access the Emails of related records from the Workflow. If you can’t, then you’ll have to write a simple logic hook.
Are you a PHP developer, or do you have one in your team?
I have a PHP developer in my team. How do we go about creating the logic hook you mentioned?
The two essential chapters to read in the Developer Guide are these:
https://docs.suitecrm.com/developer/logic-hooks/
https://docs.suitecrm.com/developer/working-with-beans/
… though reading the entire guide wouldn’t hurt 
What you would need to do (probably) is to write an after_save logic_hook on the Cases module and in it, do your magic.