Of the nine countries that currently have a nuclear arsenal, how many of them designed and built their own nuclear warheads, and if they received assistance, to what extent?
This depends very precisely on what defines "assistance" as being. For example:
The United States had many immigrants/refugees from Europe in its Manhattan Project. They also had the participation of a few dozen British scientists (some of whom were refugees from other European countries working in Britain), and had arrangements for some research to take place in Canada. They used raw materials (uranium) from Canada and the Belgian Congo.
The Soviet project benefited from Anglo-American espionage information which they used as a guide and check on their program, and they also had many project participants who had been part of the former Nazi-controlled states (Germany and Austria).
The United Kingdom had the benefit of their previous participation in the Manhattan Project with the United States.
The French had some experience derived from their participation in the Canadian part of the US-UK Manhattan Project, though this was mostly on the production side of things.
The Chinese had some early aid from the Soviet Union, but after the Sino-Soviet split, the USSR pulled out of the country and took much of its equipment and knowledge with it, and the Chinese had to re-learn most of it from scratch on their own.
The Israelis received assistance from the French in the construction of their first nuclear reactors; it is unclear how much additional assistance was given in terms of the weapons program. They may have engaged in clandestine means of acquiring materials and knowledge from other nations, and there have long been rumors that some prominent American scientists gave them some amounts of information.
India used an unsafeguarded nuclear reactor built for them by the French to generate its plutonium for the bomb.
The South Africans likely collaborated with the Israelis in several aspects of their mutual nuclear projects.
Pakistan used technology stolen from the Dutch to develop its centrifuges, and was given some forms of assistance — details quite vague — from China.
North Korea had "peaceful" assistance from the Soviet Union in developing its first reactors, and purchased centrifuges from the Pakistani metallurgist A.Q. Khan.
The above is not inclusive of all possible definitions of "assistance" in all cases but you can see it is complex. It is also, of course, hampered by secrecy. I would add that all countries also all benefited from the open publication of information of relevance on this over time; the US benefited from pre-war international publications on fission, all post-1945 countries benefited from US releases (like the Smyth Report); and over time more and more information was declassified and published, so that, for example, the French were able to determine what solvent the USA used to extract plutonium by compiling a bibliography of all information about solvents that had been published and then going through them each methodically until they found the one that worked best (and they had heard, through a rumor, that one was much better than the others). So in a sense, the international community of science, even with secrecy, gave "assistance" of some form to all of them.
The best overall book on this history is Richelson's Spying on the Bomb, which just has lots of details on various programs, but Kroenig's Exporting the Bomb also has good case studies on states that help other states get nukes.