I'm new to DDD and I want to clearly understand each domain object structure and role
Your best starting point is "the blue book" (Evans, 2003).
For this question, the two important chapters to review are chapter 5 ("A model expressed in software") and chapter 6 ("the life cycle of a domain object").
ENTITIES and VALUE OBJECTS are two patterns described in chapter 5, which is to say that they are patterns that commonly arise when we are modeling a domain. The TL;DR version: ENTITIES are used to represent relationships in the domain that change over time. VALUE OBJECTS are domain specific data structures.
AGGREGATES and FACTORIES are patterns described in chapter 6, which is to say that they are patterns that commonly arise when we are trying to manage the life cycle of the domain object. It's common that modifications to domain entities may be distributed across multiple sessions, so we need to think about how we store information in the past and reload that information in the future.
The only contact point the client can interact with the domain objects, the client should not be able to modify or create new Entities or value objects whiteout the aggregate root?
Gray area. "Creation patterns are weird." The theory is that you always copy information into the domain model via an aggregate root. But when the aggregate root you need doesn't exist yet, then what? There are a number of different patterns that people use here to create the new root entity from nothing.
That said - we don't expect the application to be directly coupled to the internal design of the aggregate. This is standard "best practice" OO, with the application code coupled to the model's interface without being coupled to the model's implementation/data structure.
Can an aggregate root contain only value objects ?
The definition of the root entity in the aggregate may include references to other entities in the same aggregate. Evans explicitly refers to "entities other than the root"; in order to share information with an entity other than the root, there must be some way to traverse references from the root to these non-root entities.
Shall the entities contain only value objects?
The definition of an entity may include references to other entities (including the root entity) in the same aggregate.
shall I go ahead and encapsulate every primitive type in an value object?
"It depends" - in a language like java, value objects are an affordance that make it easy for the compiler to give you early feed back about certain kinds of mistakes.
This is especially true if you have validation concerns. We'd like to validate (or parse) information once, rather than repeating the same check every where (duplication), and having validated vs unvalidated data be detectably different reduces the risk that unvalidated data leaks into code paths where it is not handled correctly.
Having a value object also reduces the number of places that need to change if you decide the underlying data structure needs improvement, and the value object gives you an easily guessed place to put functions/methods relating to that value.
Factories: Do I really need them?
Yes, and...
I can go ahead and write an static method within the domain object
... that's fine. Basic idea: if creating a domain object from so sufficient set of information is complicated, we want that complexity in one place, which can be invoked where we need it. That doesn't necessarily mean we need a NOUN. A function is fine.
And, of course, if your domain objects are not complicated, then "just" use the objects constructor/initializer.
