If I share a drawing in Home, and then move the drawing into a folder, will it affect other shared user?
No. Likewise, other shared users can do the same and it will not affect your drawing either.
If I reorganize the drawings into folders in a team, will it affect other team members?
Yes. Addition, removal and reorganization of drawings, folders, stencils, plugins and templates in a team affects all team members.
What happens if other shared users trash the drawing I shared to them from Home?
You may or may not be affected depending on the permission of the user who trashed the drawing. If the user has Owner permission, all shared users will have the same drawing trashed as well. Otherwise, your drawing will not be trashed.
Can the user create a new drawing from the drawing I shared to him/her?
Yes. All users with Owner or Edit and share permission to the drawings in their Dashboard (E.g. Home or in Team) can duplicate said drawing.
Access secondary tools by pressing the shortcut key until you reach the tool. E.g. access the freeform tool by pressing the CTRL/CMD + 4 4 times.