It is possible to move buildings. You could find the button for this next to the "build street button". Small objects you could move easily, bigger buildings, like houses, needs time and workers for the move. Only the town hall you can´t move. You can´t move streets. Streets have to be destroyed and build again.
P.S.: I hope it´s possible to understand, my English is not the best.
Also, not every building needs a street. Actually, only the town house and production buildings have to be connected by streets, all the rest you can build just filling open spaces.