Can you erase the hard drive in Recovery Mode with File Vault turned on?

You shouldn't have any problem. With FileVault turned on, Recovery HD won't appear when you press Option key, but you can access to it pressing Command and R keys while your Mac is starting

Not in Disk Utility. You would have to decrypt the volume first, or else use a shell command.

Time to update your profile, please.

How do you decrypt?

You can not use the recovery drive itself to reinstall OS X, but you can reinstall OS X without de-encrypting the drive.

WARNING: following these steps will remove all data from your harddrive. This process will in all likelyness not be reversible. Use at your own risk.

1. Prepare a recovery USB stick [1].

2. Boot from this stick

3. Start Disk Utility

4. Select the hard drive

5. Select the Partition tab

6. Change Volume Scheme to 1 Partition

7. Enter Macintosh HD in the name field

8. Click Apply

Your hard drive is now empty, you can use the installer on the same USB stick to re-install a clean OS X on your machine.

[1] http://support.apple.com/kb/dl1433