First of all, you must understand that Core Data is a object oriented persistence layer and not simply a database. Here you must switch your thinking from records, joints and queries to object oriented design.
Here I'm trying to answer your questions:
1. What is the equivalent of primary key in core data?
Core Data has its own primary key system. Each object is identified by a unique "ObjectID" that will be used as primary key internally.
You can define as many attributes in your entities and use them as "primary keys". However you won't be able to make your "record" (object) unique as it has no sense that a "object with a specific property is unique". This kind of logic is you who must add it programatically.
2. What is the eqivalent of the foreign key in core data?
A foreign key is represented in Core Data by a relationship. There are one-to-one relationships and one-to-many relationships. This means that an object can have a pointer to another object (therefore, in the database you would have a "foreign key") or an object have a collection that contains other objects (an array for example) (therefore, in the database you would have an extra table to represent this structure).
3. How do you ensure that record is unique in the table?
As mentioned above, you can't. In CoreData you have unique objects (NSManagedObject) per each context (NSManagedObjectContext) but you cannot control that an object with an specific attribute is unique among your other objects.
4. Can anyone clarify the design concept in core data database?
As said in the introduction, here you should not think in terms of databases. Core Data is an oriented object design persistence framework.
Core Data is not a simple thing that is fast learned. You need to spend some time to understand what you can do and most important, why and in which cases you should do it.
I highly recommend you to read the Core Data Programming Guide:
https://developer.apple.com/library/mac/documentation/Cocoa/Conceptual/CoreData/cdProgrammingGuide.html
Hoping to be helpful,
Joan