Not a complete list but:
Germany
Poland
Finland
Ukraine
Belarus
Latvia
Hungary
Slovakia
Estonia
The Netherlands
Denmark
France
Britain (the Channel Islands)
Russia
Romania
Greece
Italy
Austria
Yugoslavia
52
because it was awsome
There wasn't really an exact amount.
Untied States was one of the many countries whom at at first did not help during the holocaust
Russia, America, Canada, Sweeden, Austrailia, Africa
because they were looking after their own people
Please see the related questions.
Yes, there were Mexicans involved in the Holocaust, as well as numerous other nationalities. Also, some Holocaust survivers left Europe, and immigrated to Mexico and other Latin American countries.
The holocaust began almost as soon as Hitler invaded Poland. It began in small ways and then grew. Most of the world was involved in WW2. Some of the countries that fought with Germany were:ItalyJapanAlbaniaBulgariaFinlandHungaryRomaniaThailand
This depends upon where you are; the laws/restrictions in countries affected by the Holocaust have stricter terms. Countries who were not involved like the USA or China have no restrictions.
The Holocaust would not have happened were it not for the war. The war not only promoted the conditions to produce the Holocaust, but it also provided a shroud to cover the actions produced in the Holocaust.
It depends on what you mean by involved. Some Jews from Vichy controlled French North Africa were handed over to the Nazis, but apart from that active involvement did not extend beyond Europe. However, it you include countries that refused to accept refugees, then one can make out a case to the effect that most countries were in some sense involved by default.