First question: Can I put dates on the x-axis? i.e: may-25-1980, may-26-1980 (QString format) or can I only have double values on the x-axis?
Overload QwtScaleDraw::label().

Second question: Is there a way such that qwt does not copy the data, when plotting to a curve? I already have the data in my own containers
The curve gets its values using an abstract interface called QwtData. You are free to implement whatever you want behind this interface.

Uwe