I did sync my iPod with iTunes, but I can't see where are my videos on iTunes (videos I recorded using the iPod). Any hint?
On a Mac running at iTunes 11.1.3 there is a way to transfer videos to/from your iPad/iPhone (with iOS7, and maybe iOS 6).
Connect your device to your Mac and then select the device. Go to the Photos tab and check sync Photos. Underneath there will be a checkbox for Include Videos. I have my videos sync with iPhoto. Once they are in iPhoto, just drag the video to the desktop to use as you want.
iTunes doesn't sync videos/photos back from your device. The Photos tab in iTunes for the device is only for syncing photos/videos from an iPhoto/Aperture library or folder to your device. It doesn't sync the other way — from your device to the library/folder.
You need to use something like iPhoto/Aperture or Image Capture.
Transfer images and other items from your device
Transfer images, video clips, and MP3 sounds to your computer from many cameras and devices that contain a camera, such as your iPhone. Once you transfer the items, you can delete them from the device.
Connect your device to your computer, then turn the device on.
If the device is locked with a passcode, enter it.
In Image Capture, select the device in the Devices list.
Use the buttons at the bottom of the Image Capture window to view the thumbnails as a list or as icons to change the size of the thumbnails, or to rotate or delete images.
From the Import To pop-up menu, choose where to save the images or which app to use to open the image.
To import only some of the photos, select those photos, then click Import. To import all the photos, click Import All.
Choose AutoImporter from the “Connecting this [device] opens” pop-up menu to transfer images from a device to your computer whenever you connect it to your computer.
Select “Delete after Import” to remove the items from the device after transferring them to your computer. You can also select individual items on your device, then press the Delete key on your keyboard.
Source: OS X Image Capture Help