I need to know what design patterns are included in MVC, because I've checked out online that this MVC pattern uses Observer, in order to notify the view from changes in the model.
Is there any other pattern included, like Composite, Strategy or even Mediator?
What happens if we take out the Observer pattern from MVC? Does it still work? How would it change?
No there are no other patterns defined as part of MVC or MVC-inspired design patterns. You can use decorators, factories or others as part of it, but they integral parts.
The MVC design pattern is not about implementation details but about separation of concerns. You separate presentation logic from domain business logic. And you separate Interface from user input handling. You really should read GUI Architecture by Martin Fowler. That might lift some confusion.
If you take classical MVC pattern and remove the observer from it, you get Model2 MVC pattern. This is the closes you can use when it comes to web applications.
Then you also have MVP and MVVM patterns, which both differ from classical MVC and Model2 MVC by having passive views, that do not request information directly from model layer.