Part 2 is easy enough, but let’s tackle part 1.
Fusion bogs down with heavy complicated sketches, every article added has to be treated for constraint and geometry errors, so how complicated is the logo, without seeing an example, too hard to advise.
As your sketch gets bigger you don’t want to then mirror the sketch, mirror the bodies much quicker response times. So body mirror needs a face or plane as the divider.
So Using the crescent object to help describe it, the line extrusion, for height, then Thicken that body, to suit. When done, save the file. There are a few different ways to transfer the logo between files, Derive would be one way, but until your done with an early example, go with insert.
The logo component can now be inserted to the file that the box resides. It will be a new component in that file, place it straight away, you then Combine Cut the new component out of the box’s face, provided the placement resulted in an embedding by how much, etc.
if your data is sensitive, make a dummy example, describing how much bigger the true file would be. File > Export and attach to another message.
