I just need to know if all existing rules, triggers, formulas, etc. will apply to any new app created in my org. This is what I mean by App:
What is the benefit of using the standard Sales app over creating any new customized one?
Workflows/Process Builder/Apex Triggers specific to an App the person is using, or do they apply to all Apps?
Ans is. Yes, it is applicable to all the Apps.
Those rules are applicable to specific Objects. If we need to access objects from UI, we create tabs and you may think the
App is a container of all these tabs.
App is the group of tabs which is necessary for your/customer's benefit.
If, business need can be fulfilled by using standard Sales App then it's better to use standard one.
But, for other customized applications, other than Sales we need to create a separate App and give permissions to specific profiles who will be using those.