How do I allow users to rearrange the fields order during content creation? Assume I have a content type with fields a, b, c.

How to allow users to rearrange fields (when they create one content) if they want to display fields in another order? Like b,a,c or c,b,a, etc ...

EDIT:
Panelizer do the job for my case.
There is a bug when trying to save the display. But getting both the Panels and Panelizer modules in latest dev version fixed it.
If you want per-node changing of field display order I recommend looking at Panelizer module. It takes over view modes at the level of entity bundles (content types) and additionally individual entities.

It is not an exact fit of what you describe in that:


It works on an interface separate from content creation.
It is view
mode specific. So rearranging one view mode (teaser) will not change
the full view mode. That might be good or bad depending on what you
want.