No, a crossover cable is not the same as a straight-through cable..
Some network devices are able to detect crossover/straight cables and adjust their signals accordingly so you can use any type of cable, but that is more of an exception than a rule.
A crossover cable is really only designed to network two computers (only) It allows the two to be differentiated and share an Internet connection.Your machine worked because it is connected alone.You would not get any problems until you joined a Domain or Workgroup behind a switch or router.
All 8 wires are needed for gigabit ethernet. You can also put two fast ethernet links through one cable. Or use the same cable for ethernet and telephone.
A crossover cable was originally meant to uplink hubs and switches.
Ethernet has nothing to do with internet.