A partial answer regarding whether Office 39 exists and finances the nuclear program.
No doubt Office 39 does indeed exist. Following Executive Order 13551 US Treasury has frozen their funds a year ago.
The U.S. Department of the Treasury today designated Korea Daesong
Bank and Korea Daesong General Trading Corporation pursuant to
Executive Order (E.O.) 13551 for being owned or controlled by Office
39 of the Korean Workers' Party. Office 39 is a secretive branch of
the government of the Democratic People's Republic of Korea (North
Korea) that provides critical support to North Korean leadership in
part through engaging in illicit economic activities and managing
slush funds and generating revenues for the leadership. Office 39 was
named in the Annex to E.O. 13551, issued by President Obama on August
30, 2010, in response to the U.S. government's longstanding concerns
regarding North Korea's involvement in a range of illicit activities,
many of which are conducted through government agencies and associated
front companies. Korea Daesong Bank is involved in facilitating North
Korea's illicit financing projects, and Korea Daesong General Trading
Corporation is used to facilitate foreign transactions on behalf of
Office 39.
However, I couldn't find any claim that Office 39 finances N. Korea's nuclear program. Most sources suggest that it manages leaders' private slush funds and imports embargoed luxuries for them.
AOL News:
According to the State and Treasury Departments, Office 39 --
officially part of the Korean Workers Party -- manages the
"leadership's slush funds," generating foreign currency and using
branches all over the country to distribute the luxury goods that
maintain the loyalty of top officials -- and that the U.N. Security
Council has tried to ban from North Korea for just that reason.
Reuters:
It has branches throughout the nation that raise and manage funds
and is responsible for earning foreign currency for senior party
leaders through illicit activities such as narcotics trafficking.
Office 39 controls a number of entities inside North Korea and
abroad through which the Treasury says it is involved in the
production, smuggling and distribution of narcotics and it has also
been involved in the attempted procurement and transfer to North Korea
of luxury goods.
It produced methamphetamine and was also involved in its supply to
small-scale North Korean smugglers for distribution through China and
South Korea. It also operates poppy farms and produces opium and
heroin, the Treasury says.
In 2009, Office 39 was involved in the failed attempt to purchase
and export to North Korea -- through China -- two Italian-made luxury
yachts worth more than $15 million and destined for North Korean
leader Kim Jong-il, the Treasury says.