Can you play online for all PS3 games using a wireless network?

May be...

The reason I ask is because I am noticing some games that say "Ethernet Connection required for online play," and others that say "Broadband connection required for online play." By ethernet connection, dose that mean I cant play online unless the PS3 is connected directy to a router? and I cant play online using wifi?

by ethernet it means you need to connect it to the router/modem

by broadband it means you need high speed internet connection.

Also, you can use a PS3 wifi adapter to play online. :)

no, because not all games have online play some of them do

you can play using either a wifi connection or ethernet cable