Is it permissible for a woman who lives alone and fears for her safety due to the easy accessibility of her apartment to acquire a dog for guarding inside the apartment, while ensuring the dog is kept away from clothes and the prayer area?

It is permissible for a woman to live alone in an independent house if she is safe therein; otherwise, it is forbidden.

As for owning a dog, the default ruling is prohibition, except for a dog used for livestock, hunting, or farming. It is permissible to keep a dog for guarding when needed, provided that it does not enter the house and is not touched. If its saliva touches something, it must be washed seven times, one of which is with earth.