Why does my Pug's tongue hang out, making it hard for her to chew?

Very cute puppy. It is possible that she is sticking out her tongue due to positioning of her teeth. IF she were to have malocclusion (teeth abnormally positioned) it could allow her tongue to slip out. It could also just be a puppy things she grows out of. Good luck with the puppy

He has a very short snout, so this may be because his tongue is too long and there is not enough space for his tongue inside the mouth. This is very likely, especially if he can freely move his tongue. If his tongue appears paralysed you need to take him to your veterinarian for an exam to find out why. There could be various reasons for this.

Puppies this small don't have teeth to keep the tongue in the mouth, so it's common to see them sticking their tongue out a little. However, this does seem to be out a little more than normal, which may indicate that he has an overly large tongue for his snout. I wouldn't worry too much about this right now unless he is having difficulty suckling or other issues. It's definitely possible that it won't stick out as much as he ages. You can have the vet evaluate him better when you take him in for his first vaccines around 6-8 weeks of age. I hope that helps and all is well with your pup.

Usually when a dog can only stick his tongue to one side it's either a structural problem of the mouth cavity or a neurological problem (in the brain), i would recommend taking him to the vet in order to have this issue checked, i'm not sure there will be a solution for this problem though.

This situation does present challenges. Certainly keeping her lean is best for her in the long run. Too much added fat just makes breathing more difficult. A picture of your dog was not included, so I am not sure what her nose and nostrils look like, but a surgical procedure can be done to make the opening of the nostrils wider if they are very constructed. This can improve their ability to breathe without having to open mouth breathe. If your vet has never mentioned it, or maybe does not do the procedure-many vets do not- you can ask them for a referral to a veterinary surgeon who does. The surgery is basically like a cosmetic surgery but the benefits can be great. Other things to do are to reduce the humidity in your home, use a light fan where she rests, don't walk her too far or during hot parts of the day. It's great that she has a mom who is so willing to help her.

Depending on which teeth and how many are removed it is not uncommon for some dogs to not be able to keep their tongue in after extractions. This can also be a nervous behavior or a sign of nausea. It is unlikely neurological if there are no other signs such as difficulty swallowing or blinking or any changes in facial symmetry

That is unusual. It could be that her tongue is ‘tied’ meaning it has an attachment further up the tongue than normal and she can’t extend it. Your doctor may be able to see it but if Avery is very wiggly, she might have to be sedated to get a good view. There may be a surgical option to fix this. Try feeding her out of a treat ball. She will have to roll this ball around to get the kibble out so it will slow things down. Make sure she can pick the kibble up off the ground as well. I hope this is helpful and please feel free to post any additional questions!