Parent theme not updating?

The way I understood this is that one creates a child page – does all the editing there and the parent is automatically being updated with this content and formatting – but not permanently? Then when you install an update to the parent, the parent goes back to default and you reactivate the Child and it inherits the parent’s new updates. Then the parent gets all the new formatting again. Automatically.Is this correct?
I have been building my site on the child theme. I went to the parent and activated it (wanted to fetch a template) and saw that the header was not updated – the parent is NOT a replica of the child? I can’t understand this. Can someone please help. The rest of the site looks fine – it’s just the header and the menu bar above that are not right. I am working in Twenty Twelve.
Also – once I have built the site – is it the parent I activate? The child being a reserve …
Thanks in advance.