How can I get Overpass-API to just display my objects with just one tag ?

I don't know if overpass API can count tags. Neither do I know if you can query "your" objects.

If you are looking for buildings wighout house numbers, you could either use Simon's no address layer or you could use this overpass query (objects that have a building tag set and don't have an addr:housenumber tag):

(
 node({{bbox}})["building"]
  ["addr:housenumber"!~".*"];
 way({{bbox}})["building"]
  ["addr:housenumber"!~".*"];
 rel({{bbox}})["building"]
  ["addr:housenumber"!~".*"];
);
(._;>;);
out;

HTH /al

A combination of the difference operator and regular expressions for keys can make this happen. Unfortunately, you cannot use negative look-ahead (?!) for regular expressions, which makes the whole story very complex (see this stackoverflow post on how to build such an expression).

That's why I resort to a simplified approach and exclude buildings, which have any tags that don't start with a letter "b". However, the basic principle is the same.

[bbox:{{bbox}}];
((
// retrieve all buildings    
  way[building=yes];
// and remove...    
  - 
// all buildings which also have a tag not starting with "b"    
  way[building=yes][~"^[^b].*$"~"."]; 
); >; );
out;

Try in Overpass Turbo: http://overpass-turbo.eu/s/4Z9

http://overpass-turbo.eu/s/rjM has an example of query that is using tag counting. It will find poorly tagged object - with only tourism=attraction or tourism attraction + name tag in Poland,

/*
This has been generated by the overpass-turbo wizard.
The original search was:
“addr:housenumber=* and name=* and type:node and aeroway!=* and amenity!=* and craft!=* and historic!=* and leisure!=* and man_made!=* and office!=* and power!=* and railway!=* and shop!=* and tourism!=* in Polska”
*/
[out:xml]/*fixed by auto repair*/[timeout:2500];
// fetch area “Polska” to search in
{{geocodeArea:Polska}}->.searchArea;
// gather results
(
  // query part for: “"addr:housenumber"=* and name=* and aeroway!=* and amenity!=* and craft!=* and historic!=* and leisure!=* and man_made!=* and office!=* and power!=* and railway!=* and shop!=* and tourism!=*”
 node[tourism=attraction](if:count_tags()==1)(area.searchArea);
   node[tourism=attraction][name](if:count_tags()==2)(area.searchArea);
);
// print results
out meta;/*fixed by auto repair*/
>;
out meta qt;/*fixed by auto repair*/

query was provided by RicoElectrico, thanks! source: https://forum.openstreetmap.org/viewtopic.php?pid=661266#p661266

I'm not sure what you mean.

Concerning the output format, Overpass API prints for an object always either all tags or no tags at all.

If you want to find an object with a certain tag but not a certain other tag, you can the solution provided by _al above.