Kate Kane is best known as Batwoman who operates under the cape and cowl with ties to the Bat-Family.
- Born to the Kane family, along with her twin sister Beth; the first twelve years were pretty happy and uneventful, until everyone but her father Jake was kidnapped one day by terrorists.
- Jake Kane managed to find his family, but his wife was executed and Beth was seemingly killed in the crossfire between the kidnappers and the soldiers who Jake brought along on the operation.
- Kate, as the only survivor, wound up enlisting in the US Military Academy, driven by the latent desire to lash out at her kidnappers and people like them.
- Kate excelled in the Academy, but her sexual orientation and relationship with another cadet wound up resulting in her dismissal; she spent the next several years doing basically nothing, though she did find the time to have and eventually ruin a relationship with GCPD officer Renee Montoya.
- Not long after breaking up with Renee, she was accosted by a mugger, who she handily put down with her military training; afterwards, she briefly encountered the Batman. The whole experience came together to show her a new way to 'serve', removed from the possibility of actual military service.
- Following some years spent stealing military equipment and settling into the idea of being a vigilante, Kate went on some night time forays and was quickly found out by her father, who promised to properly outfit her if she'd agree to be sent around the world to be trained.
- Following her training, Kate began to operate as Batwoman in Gotham City; one of her first cases involved an arm of Intergang operating as a crime-based religion in Gotham City. A bizarre prophecy involving the 'Twice-Named Daughter of Cain' led to her being captured and nearly killed by a knife through the heart.
- While she survived the experience, Kate has made it her mission to learn everything she can about the Religion of Crime in order to bring it down, along with her general mission of keeping Gotham City safe.
Following her ejection from the US Military Academy, Kate Kane spent years without much direction or purpose; a chance encounter with a mugger - who she handily subdued - and then the Batman, who helped her to her feet before going on his way set her on a course to do something more substantial with her training and her life. Since then, she's been dedicated - perhaps dangerously so, these days - to hunting out the elements of crime and corruption infecting Gotham City.
Despite having experienced the potential dangers of her chosen way of life first hand, she is without fear in stalking the streets as Batwoman--in fact, having survived the Religion of Crime has, all on its own, girded her against trepidation, as while the Penguin and Harley Quinn may be /dangerous/, it's not particularly likely that either will try to use her as a human sacrifice or anything. Despite her newness to the job, she's growing accustomed - if not necessarily appreciative - to the toll it takes on her personal life, and comfortable behind the mask of Batwoman.
When she /does/ have down time, she tries to live as normally as possible; she lacks the same level of personal trauma as some of Gotham City's heroes, which perhaps makes it easier to life with a degree of normalcy, with some separation between Kate Kane and Batwoman. She's pretty awful at managing long term relationships, keeping appointments, and things of that nature, of course, as the job is a pretty time-consuming one, and these sacrifices are generally viewed as regrettable rather than an inevitable outcome of being a heroine.
None at all, unless being able to masquerade as a pseudo-undead costumed adventurer counts.
Kate Kane spent several years in the United States Military Academy, and accordingly learned a lot about tactics, how to handle firearms, interrogation techniques, and other miscellanea. Following her discharge from the Academy, she did a lot of laying around interspersed with bouts of college--mostly to try and prepare her for overseeing the day to day operations of the Kane family business.
Once she finally found something she could latch onto in her life - playing at being a vigilante - she was whisked off by her father to trainers around the world for several years, teaching her the skills she'd need to know to survive; as a result, she's come away an expert hand to hand combatant in peak physical condition and a fairly well studied detective, to boot.
The Kane family is absurdly rich. Wayne rich, ~Stark rich~, very well off. This fortune - filtered through Kane Industries - is what allows Kate to access her state of the art equipment, most of which is stored in an underground bunker filled with high end computers and crime lab equipment to assist Kate in her crime-fighting endeavours. In addition, she owns a few vehicles - cars, planes, motorcycles - specifically for use as Batwoman, and those are kept in the complex to be driven or piloted into the city through various means of secreted egress.
Her personal equipment consists of a light-weight body armour/superhero costume with several conveniences built directly into its various accoutrements: the cape, for instance, can actually be used to glide for short distances, the gloves are ribbed for increased grip on even smooth surfaces, and they are separate from her bracers, which come with several detachable, bladed throwing weapons. Like any good Bat-person, she also wears a utility belt filled with smoke grenades, throwing weapons, grappling lines, and assorted other handheld self-defense weapons. Notably, she also carries small firearm in her back, as she doesn't carry the same trauma about firearms or cascading pearls or Crime Alley that some Bats do.
Much of her equipment was originally sourced from the US army, courtesy of her father, Colonel Kane. Her father also supervises her on missions, and sees to the maintenance of her equipment in between them.
Catherine Kane is Kate's stepmother, and is kind of a bitch; she also has some say in how freely Kate can access the family fortune, as it isn't precisely all hers, so there's some amount of putting up with Catherine's crap. Her father, while not as big a pain to deal with, does still have his hand in her crime-fighting endeavours, which can be kind of awkward; she isn't necessarily averse to going against his wishes if she absolutely must, but he's vital enough in sourcing and maintaining her equipment that things could be rocky, were his support withdrawn.
Rounding out Kate's familial woes is her sister, Beth -- now known as Alice, the mad new head of the Religion of Crime - who Kate has been chasing without much real understanding of who she is, or even her existence; she's been hunting the leader of the organization without any specifics.
As to the hunt, in the course of one of Batwoman's first cases, she was captured by members of the Religion of Crime and nearly killed by being stabbed in the heart; currently, she's in good enough shape for a woman who's survived being stabbed in the heart, but it's the kind of injury that has lingering consequences, should she push herself too hard or do anything else to aggravate the damaged muscle.
Finally, Kate's identity as Batwoman is a secret, to the point that she wears a long, red wig and lots of makeup to give her skin a ghostly white appearance when she's in costume, just to make Batwoman and Kate Kane a little harder to associate with one another.