Wrong.
Reagan was a HUGE free trader
Not precisely (he instituted a plethora of quotas and other barriers), and to the extent he was, he never did fully shake the FDR dogma he had been indoctrinated with.
Free Trade IS a conservative idea.
Wrong.
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It is by definition. Conservativism, as defined is complete economic freedom, with social limitations. Libertarianism is complete economic freeedom with no social limitiations. Liberalism is restricted economic freedom with no social limitiations. Popularism is restricted economic and restricted social behavior.
On Reagan:
http://www.cato.org/dailys/06-24-04.html
Here is another quote for you:
Let the general government be reduced to foreign concerns only, and let our affairs be disentangled from those of all other nations, except as to commerce, which the merchants will manage the better, the more they are left free to manage for themselves, and our general government may be reduced to a very simple organization, & a very unexpensive one; a few plain duties to be performed by a few servants.
-Thomas Jefferson