Nasty bug or weirdness with Project plus Offset

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I wanted to make a rectangular block with a sort of squiggle cut in one surface. Also, I wanted to work out the geometry for the rectangle and squiggle in a base sketch (or top-level sketch if you prefer) before I started creating 3D forms. Here are my steps:
1. Start new model.
2. Make BaseSketch on XY plane - a rectangle with an inscribed curve (multiple line and arc segments) as a guidline for the "squiggle".
3. Close sketch
4. Make New Component1 and make sure it is activated.
5. Make base sketch visible.
6. Make new Sketch1 in Component1 on XY plane: a rectangle snapped to the BaseSketch rectangle.
7. Extrude the rectangle in +Z direction.
8. Make new Sketch2 in Component1 on front face of extrusion (offset from XY plane).
9. Use Project to copy curve in base sketch to Sketch2 - it appears as a connected series of lines and arcs with magenta color.
10. Exit Project command.
11. Select all the magenta lines and arcs and start Offset command.
12. Set offset distance and click OK.
Result: Offset lines and arcs are created but in the wrong sketch! They appear in BaseSketch even though Component1 is active and Sketch2 is the sketch being edited. These offset entities are of no use within Component1. I guess I could use Project again to copy them back into the sketch in which I am already working. But does this make any sense as a workflow: draw in base sketch, Project to component sketch, Offset back to base sketch and finally Project again to component sketch?
Here is the link for my test model: http://a360.co/25ThRNB
Additionally:
a) Using Offset on entities created by Project seems to be hit or miss. Sometimes all the selected entities get offset and sometimes only the one. The 'chain' option does not seem to work at all for projected entities. (saunde35 has already commented on this.)
b) For Project one must start the command and then select the entities. For the conceptually similar Offset one must select the entities and then start the command. Guys!!