How will I know if my iPhone is already jailbreak?

How will I know if my iPhone 3gs is already in jailbreak?

And my iphone 3gs is already unlocked so can I install any apps on it?

You can tell by sliding to the right and typing "Cydia" into the search bar. If nothing comes up then your iPhone is not jailbroken.

Usually you can see the Cydia app sometimes with addition of installous app. Also if you try to get pirate games from pc to itunes they will successfully install on your device. As well, if you try to download something from installous the games will download. Hope that helps
P.S. Look for untethered jailbreak-tethered is a pain in the ***