ASX - Stocks eg BHP, CBA
SFE - Futures eg SPI, 10 year bonds
Now they have merged - so just ASX now.
Influence on our markets? Nil - its an exchange.
Think you're talking about the our futures (SPI), it leads the physical slightly by virtue of being updated more often than our index... In daytime, SPI and cash index will track each other, night SPI tracks US futures.
If you want to see the futures fluctuate in real time, you need a futures broker or charting package that supplies future data. ie Not Comsuc...
SFE's simulator game had live SPI but not sure if thats still up anymore.