Is it just for working out the correct play for flops, or is it used for turn and river plays also?

A nash equilibrium is when, in a non-cooperative game with rational players aware of each other's strategy, no player can improve their outcomes by changing their strategy alone. It is an application of game theory.

In theory, game theory can be used to derive the optimum strategy in any game context (preflop, postflop, heads up, multiway, etc.) In practice, the more variables (streets of betting remaining, cards remaining to be seen, players still active), the more complex the outcome tree is, and therefore the more difficult it is to apply game theory. Nash Equilibrium are primarily used for preflop push\fold charts.

"Nobody goes for the blonde"

It's actually easier to find Nash Equilibrium frequencies on the river (or with a pre-flop shove) than for the early streets.
e.g. In a toy game where one player shoves the river with a pot-sized bet, his range should be divided into value bets and bluffs in a ratio of 2:1. The other player should call with his bluff-catchers 50% of the time. Any deviation from that allows adaptive exploits.

On the early streets, ranges are so much more complicated, and there are so many variables (all the potential runouts and action sequences, due to stacks still being deep), that even the most powerful computers in the world haven't found the complete solution.
To put it another way, you can't find the Nash Equilibrium play for the flop, unless you've already worked out everything that can possibly happen on the turn and river as well.