I am stuck with the following node set expression.
  In an external document I want to find the element which name is
  'anchor' and which attribute @name has the value
  of the variable $anchor.

If I understand you correctkly you just want

<xsl:variable name="anchor-node"select="$external-doc//anchor[@name=$anchor]"/>

I in your code fragments you seem to have switched to looking for name
my-anchor rather than anchor.

3 <xsl:variable name="anchor-node" select="$external-doc//node()[name()
= 'my-anchor' and @name = $anchor]" />

that is legal but there is no need to select all nodes withg node() then
filter out those with name my-anchor, you could just do

3 <xsl:variable name="anchor-node" select="$external-doc//my-anchor[@name = $anchor]" />

which is more or less as above.

 <xsl:variable name="anchor-node" select="$external-doc//node()[name()
= 'my-anchor' and @name = @anchor]" />
or
 <xsl:variable name="anchor-node" select="$external-doc//my-anchor[@name = @anchor]" />

is also legal but tests the anchor attribute of the my-anchor element in
$external-doc is equal to the name attribute on the smae element.

David

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