If anything, they might frown upon you taking your own picture for the "entrance picture" they try to sell you (no characters - just a background). But I don't know that they're even disallowing that.
No, you are perfectly welcome to use your camera to photograph the characters. And the photopass photgraphers will gladly allow you to use your camera at at the 'entrance" pic.
Oh no, you can take pictures! They didn't even frown on us taking out own pictures at the entry. In fact, a cast member at Chef Mickey's (and Tusker House) asked for my camera so they could take a family picture for us. At 1900 PF (and Akershus) the photographer said "let mom get a picture" and directed my kid's where to look before she took the photo package pictures.
So your good...take your camera! We got some great shots at both places!
At Chef Mickey's, you are definitely allowed to take your own pics with your own camera, with the characters, of the restaurant...it is no different than taking pics in a park.
Of course you can take your own photos. Look around on these boards and you'll see plenty. Here's a few just to whet your appetite...for photos that is, you'll just have to wait on the food. Unless of course someone posts photos of their food
Not only can you use your own camera, lots of times the character handlers (ToonHeads) will take pictures of you with the characters with your camera. This happened the most at Chef Mickey. If you're lucky, Goofy might try to use (and 'drop') your camera.