@SteveKStafford
Yes, you are right. As soon as I enlarged the distance between the walls (without doors) - there was no warning anymore.
@ToanDN
Thanks, this solution enabled to "override" too tight walls next to doors.
@anze.kumar
Yes, that was the reason for warnings.
@barthbradley
So after all - your solution was applicable, I had other issues that gave me warnings. It needed a few additional steps, but it is applicable.
As for "Web-available" family:
I tried to experiment a bit with this family to adopt it to my needs. I can enlarge the door, but there is some part of the family (above the door) that stays lower, so I gave up. Additionally - the conceptual design is different - this family has much bigger region above the door (the stubborn one that won't shrink) then needed one AS-1P1S (https://www.biobase.cc/Air-Shower-pd47186305.html).
So - even if the stubborn part would change its height following the door - I suppose it would be too thick anyway (having in mind all that small rectangular shapes on the right above the door)...

As for others who might have the similar issue, a quick (?) workflow, what I ended up doing:
- make 4 walls at appropriate distance;
- make the ceiling;
- add 2 doors (if the room is too tight, follow @ToanDN's instructions and disallow join);
- make group of all elements;
move the "insertion point" of a group to the "front" of the wall;
- rotate the group if needed;
- "create similar" and select the wall to insert the group - "Highlighted walls overlap. One of them may be ignored when Revit finds room boundaries. Use Cut Geometry to embed one wall within the other, or tab-select one of the grouped overlapping walls and exclude it from the group instance." warning arise.
- ungroup (if I don't ungroup, a funny thing happens)
- use Modify/Cut Geometry (as the warning implies) and select the smaller wall from the (ungrouped) group then the wall the group is put on - this removes the "double" wall, yet the door stays on the new wall.
Group is available for additional use from the Project Browser.
-
A smooth, optimized workflow? Well - it get's the work done...
Thank you all for help.