How this negative current is converted into positive DC current?
The words are confusing, because current is induced (not
converted) by the mutual inductor, the transformer. And, 'positive'
current just means (by convention) current going clockwise in
a circuit diagram. The diagram can be drawn as a mirror-image,
without changing the circuit to which it refers, so positive
or negative current is just... a conventional direction-naming scheme.
The most important thing to notice, is that current in the load
resistor is going right-to-left when it is CW in one (the upper)
branch of the transformer output, or when it is CCW in the other
(lower) branch of the transformer output windings.
The load resistor, therefore, can be part of an active CW and also
an active CCW current-carrying secondary circuit. We
use a completely different convention when calling its
current positive or negative, and that is the right-to-left
current direction being positive.
Then you look at the rectifiers: those diodes allow only positive
current in the resistor. This, we call DC (because the resistor current does not change its direction).