whoh.. that may seem disturbing.. but i dont think dry mouth could lead to vomiting,,, that must be because of some ohter reason..
also, her snoring and all seems to indicate that her nasal passages are too narrow or are blocked by some tissues.. not much you can do about it as this age... when she grows a little older, she can learn breathing yoga exercises to stop it...
the stuffy nose seems to be because of an ever present cold...
Try homepathy treatment but you have to be very patient as it will take time for complete cure. Homeopathy is very effective for treating kids and the medicines are also very gentle on their system.