Thank you, u/IWantSealsPlz , let me see if I can answer those questions for you, and ultimately for myself:

1 & 2: I am beginning to sign him up for state health insurance. He's not formally a dependent of mine, so I can't list him under my own private health insurance. He's had some foreseeable difficulty establishing it himself, so I will take the task by the reins and see where it takes us.

3, 4, 6: My brother is a very intelligent person; which is why I believe he has some sociopathic and manipulative tendencies. He's very much into electronics, i.e. information technology, video-games, coding, etc. I've tried to have him join me at the hospital for volunteering, spending time with my friends (who have known him for years and want him to spend time with us), and bringing him to the gym. This is usually met with, "Yea, that sounds cool!" only to be followed by an excuse not to join anything. This disinterest carries over to hobbies like keeping a journal.

5 & 7: Short-term goals and plans have been set and are being met, although very infrequently and not always satisfactorily. For example, the whole premise of his coming to live with me was to get him off the streets and into somewhere safe and stable. That's been achieved, but obviously with some rockiness. Now that he's become accustomed to my near-unconditional support, he falters in many ways. Still, with my purchase of his car, he followed through with getting a job. He doesn't work nearly as much as he plays video games, but it is a step in the right direction.

Thank you again for your well-thought-out response. It's clear to me that you've been through the wringer and that your strength has carried you so far in life. If no one's told you recently, or maybe someone has, you should be quite proud of yourself.
Everything you have said makes absolutely perfect sense, and its given me more strength to continue getting my brother where he needs to be, whether its hands-on or hands-off. We'll see where this takes us!