Yes, BJTs have the same voltage drop across their junctions as common diodes, that's 0.6V à 0.7V between base and emitter, and the same between base and collector. Since they act like diodes they don't conduct in both directions if you apply a voltage across the two pins.
When you use them as a transistor, for an NPN there will flow current from collector to emitter through the base, though, so base-collector junction reverse biased are at that moment.

The arrows indicate electron flow, not conventional flow. Conventional flow is from positive to negative and is always used in circuit analysis. But conventional flow can't explain the details of the working of a transistor, so here electron flow is shown.
Also not that the collector voltage is higher than the base voltage.
The main differences between emitter and collector are doping concentration and size. The emitter is heavily doped, while the collector is lightly doped. You could try to swap them, but you'll get a very low \$H_{FE}\$, probably even less than 1.