While we may know intellectually that all things are impermanent and that every living being dies, most of us are shocked and anguished when the inevitable comes to pass.
The purpose of a Buddhist shrine or altar is to remind us of our objects of refuge—the Buddha, Dharma and Sangha— and also of our potential to attain Buddhahood by actualizing the Dharma through practice.
In a word, yes. Anxiety and other mental health issues can be overcome through studying, practicing and integrating the various methods found in Buddhist teachings, such as meditation. But for people with anxiety disorders, not a temporary worry or fear, Buddhist teachings and meditation are better used as an adjunct to other therapies and treatments recommended by qualified professionals.
The Buddha said, "Just as a monkey swinging through the trees grabs one branch and lets it go to seize another, so too, that which is called thought, mind or consciousness arises and disappears continually both day and night."