Quick answer: Only the author/creator can get copyright, so: No, this buyer does not get copyright over these works.
(The US Copyright Office has several pamphlets explaining copyright clearly and concisely. I've linked to some of them below; if you want more detail, they are the best place to start.)
Copyright v Right to Copy: Copyright is not the same as the right to copy. Copyright gives legal control over making copies to the author/creator. If a work is copyrighted, the owner of the copyright has the right to decide who can copy the work. If a work is not copyrighted, it is "in the public domain," and anyone has the right to copy it.
Is the work copyrighted? The answer depends on when it was created. In the US, the rules changed dramatically on January 1, 1978.
For works created after Jan 1, 1978, the author gets copyright once she puts pen to paper. Since then, all creative works that have been "fixed" in a "tangible form of expression," are automatically copyrighted, whether or not they are registered. (Registered works get some extra protections.)
For works created before 1978, the author got copyright after the work was published or registered. (Under the new law, works that were created before 1978 that were not published or registered before 1978 get copyright under the terms of the new law.)
Is the work still copyrighted? Again, the answer depends on when it was produced. The basic rule for works produced after 1977 is that copyright lasts until 70 years after the creator's death. The rules for works produced before 1977 are more complicated. Among other things, whether a work is still copyrighted depends on whether the copyright was renewed.
What about the heirs? Copyright is an intangible right. It passes to the heirs on the creator's death, regardless of whether they still own the tangible creation. However, the heirs only have rights over the tangible creation if they own it. If they don't, the owner of the painting or manuscript can keep any and all money he gets from selling these.
Copyright and the "bundle of sticks:" Law professors love to say property rights are like a bundle of sticks. Each stick represents the legal right to control some use of the property. In this case, whoever owns the copyright stick has legal control over copying the property. Someone else may own the actual physical property.