Buddhism as it is most often understood is that of a non-violent path based on compassion for all living creatures, but is there a Buddhism for the warrior?
Historically Buddhism has appealed to many warrior peoples. For example, the Khitan, Jurchen and Mongol steppe peoples were adept horsemen warriors who conquered vast amounts of territory, but at the same time they took an interest in Buddhism. I believe part of the reason for this is that there are multiple levels of truth in Buddhadharma, and practice isn't a matter of all or nothing. You can take refuge while forgoing precepts. As a layperson you can selectively take some precepts while not receiving the others. The philosophy is likewise available on differing levels. Moreover, the religious theatre that Buddhist traditions offer is especially meaningful. In particular, blessings and merit dedication.
Of course historically we know of Shaolin monks, the connection of Zen and the Samurai, Japanese feudal lords like Uesugi Kenshin being devout Shingon practitioners, the Japanese Sohei and Yamabushi, and Tibetan, Mongol, and Qing/Manchu Buddhists who were warriors or engaged in warfare, and of course Siddhartha Gautama himself was a kshatriya. Are all of these merely perversions or is there room for a warrior lifestyle/mindset and Buddhism?
Not formally. The first lay precept proscribes killing. That means primarily not committing homicide, but then it also entails not taking the life of insects and animals as well.
That isn't to say warriors haven't found Buddhism meaningful. Their profession is actually a wrong livelihood, but nevertheless like fishermen and butchers ideally nobody is rejected. You can still have opportunities to make merit and repent one's past transgressions in the hopes of securing an agreeable future.
In the same vein, how far is Ahimsa supposed to be taken? In popular culture there are often portrayals of Buddhists who won't even kill an insect. Is this truly the reality for Buddhists, and if so what does one then do about such creatures as mosquitoes that could potentially spread deadly diseases? How is self-defense treated in Buddhism or defense of various entities like family, friends, the Sangha, or the kingdom/state?
This is a big question and we can't really discuss an essentialist "Buddhism" here because in reality there is no such thing. There are Buddhisms
in the plural. One is true for one tradition won't be true for another.
Generally speaking, though, at a state level a lot of Buddhist ideas are impractical. You can't run a justice system without employing violence. If you have no justice system, you'll have no rule of law. Likewise you need a standing army as a deterrent against aggressors. This is why in India the Brahmins came to dominate the upper echelons of state power rather than the Buddhists: they could offer sound political advice, while Buddhists generally could not.
In the real world of saṃsāra, forgiveness, non-violence and peace policies are often irrelevant to the cold hard realities of war, piracy and criminal enterprises. In saṃsāra violence is the golden rule
and no matter how much we promote peace and loving kindness (we should), there will continue to be aggressors, tyrants and criminals.
Are we as Buddhists morally obliged to fight such forces? Well, we're not supposed to actually. To not exercise violence is virtuous, but not practical if you're running a state under the direct threat of enemies who happily will employ violence. A lot of core Buddhist ideas are politically impractical, which is why historically in many countries Buddhism existed to serve functions other than formulating useful policies for the state to pursue. There were other parties better suited to war and criminal justice than Buddhists.
At one level Buddhist institutions are, ironically, often beneficiaries of violence yet at the same time promote non-violence and renunciation of worldly pursuits. It isn't an easy position to be in. In saṃsāra nothing is so simple. The Mongols might have murdered tens of millions of people, but they invested some of their war booty in Buddhism. In Taiwan Buddhism exists largely because the communists were kept away by the threat of American intervention (the threat of violence). If the Nationalists on the mainland had defeated the communists, then Chinese and Tibetan Buddhisms would not have suffered as horribly as they did at the hands of the Chinese Communist Party.
You might argue that some faithful Buddhists might have fought the communists to save Buddhism, but then that would still be contrary to the basic teachings of the Buddha.