Please appreciate that this is written to reach out to newer S3D Users, while hopefully addressing your questions.
SKETCHES:
Sketches reside on a specific Plane within each Design.
Only one Sketch may be made on each Plane, any additions to these Sketches become part of the original Sketch on that Plane.
Separate Sketches can be made by navigating to a different Plane and creating a New Sketch.
The Planes available for use, can be seen by hitting the Navigation Cube at top right, and are:
XY plane
YZ plane
ZX plane
and
Construction Planes [CP]:
Create CP using Add > Construction Plane.
CP, Offset from any of the Main Planes mentioned above or Offset to different distances from any other Plane. [including other CP], can also contain separate Sketches.
It is strongly recommended that every Sketch is given an appropriate and meaningful name.
Such Sketches are automatically Numbered Sketch 01 and incrementally upward and few will be completely comfortable remembering what Number relates to the area of immediate concern.
FOLDERS:
At present it is not possible to C&P in the time honoured manner many of us are used to.
This may be subject to change with the arrival of iPadOS, and although there are improvements in Files [Filing features], moving portions of a .shapr File requires a routine to be followed. The routine chosen is a matter of User preference, the following is mine:
From Designs > Duplicate > immediately Rename the copied File, in this case keeping in mind what it’s purpose will be.
Open the new File > hit Items bottom left to open the fly-out > usually All Items is already present at the top, if not ensure that it is.
My MO is then to Select everything that I wish to keep by selecting within the Listing, and then checking within the Design that everything required is highlighted in light Blue.
With everything present and correct I mark up everything not needed by hitting Hide [tap the '‘Eye’ Icon to show the ‘/’ Hidden Icon] for each of the unwanted Items.
Tap on a clear space within the Design to Deselect everything.
Then Select, within the Listing, everything that has been Hidden.
Then after checking that none of the visible items are amongst the List Selection, and double checking in the Design that nothing Selected is showing, hit Delete.
It is appreciated that this seems complex [even OTT?] but I emphasise that this is only my MO, do choose what works for you. Double checking before hitting Delete is sound practice.
This sounds long winded, and may be to read, but the alternatives via Exporting still require a similar routine. In addition the alternatives have Exporting and Importing aspects.