Unfortunately, you can't find or wipe your old iPhone if you never setup and enabled Find My iPhone on the device itself. However, here's a few notes to help you out with your new iPhone:
Firstly, the Find my iPhone feature is built into the iOS operating system and is different than the Find my iPhone app that you download in the App Store. The app is for using a second iOS device to track your lost first iOS device. You do not need to use the app at all, you can instead use the »www.icloud.com
The Find my iPhone feature built into the OS uses location services and a data connection (cellular or previously connected WiFi) to remotely track your device. If the iPhone is powered off then it will not work. By default Find my iPhone is disabled and does not track you. To enable it you will need an iCloud account and enable the Find my iPhone feature in iCloud settings on the device. If you don't have an iCloud account you can create one right on the iPhone during setup. Once enabled, you can then go to »www.icloud.com
and log in to remotely track or wipe your iPhone (or use the Find my iPhone app on another iOS device).
If you have a full backup of your old iPhone in iTunes, then when you connect your new iPhone to iTunes, it will ask if you want to restore your backup. This will get you back almost all of your stuff, both settings and data like text messages, apps, etc. I'm not sure if the backup includes music and pictures. You can pretty much pickup where you left off with your old iPhone.
The reason your friend knew you were using an iPhone is because of a feature called iMessage. By default this is enabled and requires the both of you to use an iOS device and have an iCloud account. When you are using the Messages app (which previously only did SMS and MMS), it figures out in the background if your recipient is another iOS device. If the recipient is, it will change your text message into an iMessage. Visibly the chat bubble becomes blue and you'll see the text iMessage in the chat log. Everyone else gets a text message green bubble and the text Text Message in the chat log.
Behind the scenes, a text message gets sent the same way it always has: through the cellular connection. But an iMessage gets sent as an Apple Push Notification and uses the data connection (either cellular data or WiFi). So an iMessage is a data packet sent over TCP/IP through Apple's push notification network. This means that iMessages do not count against your text message limit. There are also some additional benefits, like delivery notification and read notification, so you know if the iMessage made it to the destination. You can turn on/off iMessage in Settings > Messages, as well as control read receipts.
Anything else need clarifying?--
less talk, more music