Has she had a recent wellness examination to rule out any possible medical issues that may have caused any behavioral changes, I'd begin there once medically cleared, Ask your vet to recommend a reputable behaviorist that may help guide you on how to handle this dog properly, keep in mind proper handling will be for the dogs entire life, as it's your responsibility not only to keep her safe from harm but everyone else by whatever means necessary.
Chihuahua-Dachshund is the correct spelling. Poorly bred, genetically deficient dog often results in nerve bag temperament, genetics can't be changed, only somewhat controlled by an experienced owner/handler, requiring a lot of patience, consistency and time during the dogs entire life, and should have begun the moment you brought her home as well as continual enforcing it on the as needed basis. A fearful dog is more likely to bite, will be more difficult to handle, requiring experience and knowledge.
"She is more weary" as in tired/lethargic? Again mention this to the vet. Perhaps you meant wary? Mention this to the behaviorist. As far as the nails, obviously she was never properly conditioned to allow others to handle her. It won't be easy, but you may correct this, it can be done, begin now, remember patience/consistency. Both and/or either maybe possibility "bad beginning in life/part of her personality". Personality/temperament go hand in hand, and are determined by genetics, as already mentioned. Again all of this can be changed, do nothing, it may only get worse, and someone/something may get injured.
Both "worried/depressed look" are human emotions that only humans posses, so there is no need for you to anthromorphize your dog. Dogs live in the moment, they don't have the capability to project into the future as to what may or may not happen, but they do have good memories as to what they've been subjected to in the past.
Sometimes this "worried/depressed look" is placed on dogs in an attempt to describe in human terms, anxiety and/or pain, the vet should be able to diagnose the pain aspect, the behaviorist maybe able guide you on how to handle the anxiety.