Teeth Question

Since she's from a puppy mill it's probably directly related to bad breeding. How old is she? The teeth could have never developed or they may have fallen out if she has severe dental disease, in which case it's likely that her other teeth have a decent amount of tarter and her gums are probably red and inflamed above those teeth. Another possibility is if you were not the first owner, she may have had a dental cleaning and the teeth were extracted due to damage or severe dental disease, or a misaligned bite/chewing on inappropriate materials leading to a serious wear of the teeth.
Genetics can play a pretty big role in susceptibility to dental disease and can be held accountable for teeth that never develop as well. Poodles are notorious for bad dental health, especially toys and minis. Good breeding can help to alleviate that.
Fortunately, dogs do pretty well without many of their teeth and so long as she does not have tons of tarter or gingivitis, she's probably just fine. You can soften her food with water or feed canned food instead, but most dogs do well so long as the remaining teeth are healthy.

Sounds more likely to be genetic since she's so young, then. She may have had more teeth as a pup if the deciduous teeth didn't all fall out yet. The adult teeth may have never properly formed or may never have erupted and could still be below the gumline. Either way I'd keep up with softening the food since she seems to be able to eat it better that way. Also it would be a good idea to brush her teeth daily with a dog toothpaste and brush or a dental wipe. Because she may not have the pre-molars that help her chew properly, she may be more likely to develop tarter and dental disease on the teeth she does have. But there is a genetic component to dental disease as well, and being a puppy mill dog is enough to encourage daily dental care (though all dogs should have some sort of dental care anyway).

The tarter you can see on the canine tooth in that picture won't come off with brushing, but it's not severe. Brushing daily will reduce the amount of new tarter that builds up, but once it turns from plaque to tarter it needs to be scaled to be removed.
Like you mentioned, most dogs do chew mainly with their back teeth. The front teeth and canines are used more for tearing so you don't see that so often with pet dogs. If you pull the lip back farther you may see more tarter on the back teeth even though she chews back there (chewing is good, but the idea with brushing is to remove food particles that build up on the teeth and combine with bacteria, eventually hardening into plaque). It's more common for tarter to build up heavily on the back teeth than the canines and incisors. So when you brush, be sure to get way in the back.