How does classical GR concept of space-time emerge from string theory?

First, you are right in that non-Minkowski solutions to string theory, in which the gravitational field is macroscopic, it should be thought of as a condensate of a huge number of gravitons (which are one of the spacetime particles associated to a degree of freedom of the string). (Aside: a point particle, corresponding to quantum field theory, has no internal degrees of freedom; the different particles come simply from different labels attached to ponits. A string has many degrees of freedom, each of which corresponds to a particle in the spacetime interpretation of string theory, i.e. the effective field theory.)

To your question (1): certainly there is no great organizing principle of string theory (yet). One practical principle is that the 2-dimensional (quantum) field theory which describes the fluctuations of the string worldsheet should be conformal, i.e. independent of local scale invariance of the metric. This allows us to integrate over all metrics on Riemann surfaces only up to diffeomorphisms and scalings, which is to say only up to a finite number of degrees of freedom. That's an integral we can do. (Were we able to integrate over all metrics in a way that is sensible within quantum field theory, we would already have been able to quantize gravity.) Now, scale invariance imposes constraints on the background spacetime fields used to construct the 2d action (such as the metric, which determines the energy of the map from the worldsheet of the string). These constraints reduce to Einstein's equations.

That's not a very fundamental derivation, but formulating string theory in a way which is independent of the starting point ("background independence") is notoriously tricky.

(2): This goes under the name "strings in background fields," and can be found in Volume 1 of Green, Schwarz and Witten.