Scrum Teams are self-organizing and cross-functional. How the Scrum team is cross-functional?

Perhaps a distinction can be drawn between a cross-functional team in which all of the necessary skills are to be found, and a cross-skilled one in which each member can perform all types of work. 

Yes. As can be seen, The Development Team members can work on the "Product Backlog management" as stated in the scrum guide - "The Product Owner may do the above work, or have the Development Team do it.".

That means "The Development Team" have the ability to perform the tasks of Product Owner by the vice-versa is not true.

In general "The Development Team" is more Cross-functional than other two members of the Scrum team namely "Product Owner" and "The Scrum Master"

That means "The Development Team" have the ability to perform the tasks of Product Owner by the vice-versa is not true.

In general "The Development Team" is more Cross-functional than other two members of the Scrum team namely "Product Owner" and "The Scrum Master"

Really, those are rather sweeping generalisations. It depends on the team members at hand. There are developers (especially those new to Scrum) who may be lacking the skills for Product Backlog management. On the other hand, a Product Owner who used to be a developer might indeed be able to perform development work, but is generally not expected to do so, as Product Owner is usually considered to be a full time job. The same goes for Scrum Masters (though there are companies who expect Scrum Masters to participate in development).

Scrum Master and Product Owner require distinct skills which are vastly different from those of the developers. A PO will need a deeper understanding of the domain and the market than the developer. Being a Scrum Master needs a special set of social skills not everyone has. However, the cross-functional skills needed in the development team are usually of a technical nature and easier to cross-pollinate (for lack of a better term) than the special skills of PO and Scrum Master.

The team as a whole must have the skills and knowledge required for the work...including the ability to recognize where they need help.  No rules say how many skills any one member has to have, but it is important that they know what they can rely on each other to do.  I can't imagine a team where everyone has the same skill set -- that seems like both waste and massive conflict waiting to happen. 

My ideal cross-functional team has a few people who can do really, really difficult coding; someone who can build beautiful, usable pages; someone who is good with application flow; everyone needs to know data modeling, half of them need to be really good with data, and we need one data rock star.  I like to have someone who can power through a LOT of feature requests all over the application and someone who can spend six months or more evolving one module.