I unpublished most of the fields I don't need...
And I left the most desired functionality: add CV file... which doesn't work.
In the popup window can see "CV file" title - twice!
O.K. button and nothing else.
The same popup window seems to work in the frontend...
...but It's not bug free as well.
I can't upload any CV because:
1. Unsupported file type. I tried with jpg and pdf... weird. It is written that both file types are acceptable.
2. 500 KB for A4 jpg file might be not enough... Most of the people while scanning documents, don't bother with scanner settings and they have no clue how to reduce the file size.