Your posts is a little bit disjointed to me.
I don't get the correlation between the fact that you sync to your Mac and now it isn't working. That makes it sound like the Mac caused some sort of problem and that's pretty unlikely ...if that was you even mean.
Then you say the iPad will work for about 5 minutes, but all of the photos have been deleted and that iTunes tells you that you have run out of storage space .... But on what, the iPad or the Mac?
It's all a bit confusing and if you could repost and explain it a little more clearly, it would help.
Much better. Don't know if I can help, buy I'm going to try.
Try closing all the apps on your iPad. Then reset the device. See if that let's the iPad operate normally again, but don't launch the photos app yet. The iPad shutting down when you use the photos app is really odd.
To close an app, drag the app up from the multitasking display. Double tap the home button and you will see apps lined up going left to right across the screen. Swipe to get to the app that you want to close and then swipe "up" on the app preview thumbnail to close it.
Reset the iPad by holding down on the sleep and home buttons at the same time for about 10-15 seconds until the Apple Logo appears - ignore the red slider if it appears on the screen - let go of the buttons. Let the iPad start up.