To address the issue of removing doi,issn, and url one can load the xpatch packages (i.e., \usepackage{xpatch}) and then use
\xpatchbibdriver{set}
{\printfield}
{\clearfield{doi}\clearfield{issn}\clearfield{url}\printfield}
{}
{}
Here is a solution to cite all authors in an entryset. The field labelname is created when parsing the bib files to create the bbl file. In bbl contains the information only about the authors of the first entry in a set. However, the bbl files contains \set{key1,key2,...} where each keyN is the key for an entry in the entryset.
The idea is then to use the keyN and to use them to create a list of all (author) names in the entryset.
We start by creating such a list, and at the same time we create two counters to hold the total number of authors and the counter for the current author.
\newcommand{\AuthorList}{}
\newcounter{AuthorSetCount}
\newcounter{CurrentAuthorSet}
These the counters are use to parse the elements of the author list and to insert the proper delimiter between authors. They are used as follows:
\newcommand{\mycount}[1]{\addtocounter{AuthorSetCount}{1}}
\newcommand{\myitem}[1]{#1
\addtocounter{CurrentAuthorSet}{1}
\ifnumequal{\value{CurrentAuthorSet}}{\value{AuthorSetCount}}
{\addspace}
{\ifnumequal{\value{CurrentAuthorSet}}{\value{AuthorSetCount}-1}
{\addcomma\finalnamedelim}
{\addcomma\addspace}%
}%
}
To populate the list, we parse a name list. This is done by providing a formatting directive
\DeclareNameFormat{myentryset}{%
\ifinlist{#1}{\AuthorList}
{}
{\listgadd{\AuthorList}{#1}}%
}
The information in \set{...} is used by the biblatex command \entryset{}{}
where the two arguments are for pre-code and postcode. Unfortunately, for each entry in the set \entryset processes the driver for the entry. Thus we have to disable this and instead we populesate the list of author in the entryset. We introduce a conditional in the definitions of the commands used by \entryset to guard the operation when called in a citation or called in the bibliography. In a citation we execute the formatting instruction to populate the author list, otherwise the driver for the current entry is used.
\makeatletter
\def\blx@entryset#1{%
\blx@ifdata{#1}
{\begingroup
\blx@imc@clearlist{pageref}%
\blx@getdata{#1}%
\blx@setoptions@type\abx@field@entrytype
\def\abx@field@entrysetcount{1}%
\blx@entryset@precode
\ifcitation{\printnames[myentryset]{author}}% Modified lines
{\blx@driver{\blx@imc@thefield{entrytype}}}% Modified lines
\blx@entryset@postcode%
\endgroup}
{}%
\let\do\blx@entryset@i}
\def\blx@entryset@i#1{%
\blx@imc@entrydata{#1}{%
\blx@entryset@precode
\ifcitation{\printnames[myentryset]{author}}% Modified lines
{\blx@driver{\blx@imc@thefield{entrytype}}}% Modified lines
\blx@entryset@postcode}}
\makeatother
The final step is to create a specialised cite command
\DeclareCiteCommand{\CiteAllAuthorsInSet}{}{%
\ifentrytype{set}
{\entryset{}{}
\setcounter{AuthorSetCount}{0}
\forlistloop{\mycount}{\AuthorList}%
\forlistloop{\myitem}{\AuthorList}%
\setcounter{CurrentAuthorSet}{0}
\renewcommand{\AuthorList}{}}
{\printfield{labelname}}%
}{}{}
Use
\begin{document}
\par \CiteAllAuthorsInSet{Iftimie} wrote some papers \dots
\par \citeauthor{Iftimie} wrote some papers \autocite{Iftimie-LargeTimeBehavior2003,Iftimie.etal-largetimebehavior2003}. Then another \autocite{Iftimie.Kelliher-RemarksVanishingObstacle2009}.
\printbibliography[heading=subbibliography,title={References},segment=1]
\end{document}
to see the difference between \citeauthor and \CiteAllAuthorsInSet.

Here is the full code
\xpatchbibdriver{set}{\printfield}{\clearfield{doi}\clearfield{issn}\clearfield{url}\printfield}{}{}
\makeatletter
\def\blx@entryset#1{%
\blx@ifdata{#1}
{\begingroup
\blx@imc@clearlist{pageref}%
\blx@getdata{#1}%
\blx@setoptions@type\abx@field@entrytype
\def\abx@field@entrysetcount{1}%
\blx@entryset@precode
\ifcitation{\printnames[myentryset]{author}}
{\blx@driver{\blx@imc@thefield{entrytype}}}%
\blx@entryset@postcode%
\endgroup}
{}%
\let\do\blx@entryset@i}
\def\blx@entryset@i#1{%
\blx@imc@entrydata{#1}{%
\blx@entryset@precode
\ifcitation{\printnames[myentryset]{author}}
{\blx@driver{\blx@imc@thefield{entrytype}}}%
\blx@entryset@postcode}}
\makeatother
\newcommand{\AuthorList}{}
\DeclareNameFormat{myentryset}{%
\ifinlist{#1}{\AuthorList}
{}
{\listgadd{\AuthorList}{#1}}%
}
\newcounter{AuthorSetCount}
\newcounter{CurrentAuthorSet}
\newcommand{\mycount}[1]{\addtocounter{AuthorSetCount}{1}}
\newcommand{\myitem}[1]{#1
\addtocounter{CurrentAuthorSet}{1}
\ifnumequal{\value{CurrentAuthorSet}}{\value{AuthorSetCount}}
{\addspace}
{\ifnumequal{\value{CurrentAuthorSet}}{\value{AuthorSetCount}-1}
{\addcomma\finalnamedelim}
{\addcomma\addspace}%
}%
}
\DeclareCiteCommand{\CiteAllAuthorsInSet}{}{%
\ifentrytype{set}
{\entryset{}{}
\setcounter{AuthorSetCount}{0}
\forlistloop{\mycount}{\AuthorList}%
\forlistloop{\myitem}{\AuthorList}%
\setcounter{CurrentAuthorSet}{0}%
\renewcommand{\AuthorList}{}%
}
{\printnames{labelname}}%
}{}{}
\nodriveris a very neat solution. Though, the solution does not combine all the authors in a group in a single list (not sure whether this is what the OP wants). – Guido Mar 24 '13 at 05:45\AtEveryBibitemdirectives I may add (I also suppress month fields f.ex. for which there is no package option like there is for doi/url/isbn), but Guido's answer addresses the second one better, IMHO. Should I split my question into two? And let Guido move his answer to the second question? – Christoph B. Mar 25 '13 at 13:35\citeauthor. The first is due to a missing%, the second generated by\entryset. I'll fix them in a bit. – Audrey Apr 02 '13 at 13:23