Yes, it is possible to have your skydive filmed and photographed. For the tandem skydive your camera flyer will exit the aircraft with you to capture your free fall experience. Also there is a hand camera option, which gives you more options as filming the flying under the canopy too. As a result it is only possible for each camera flyer to film one person at a time. The video and photos will be send to you vie email link.
On the other hand no, you cannot take your own camera on your tandem skydive.