The categorical imperative (kinda) ALWAYS works for a single action, thats the real power of it. No matter the situation, applying Kants reasoning to a possible action will always give you a definite answer - Moral or Immoral.

It is actually rather easy to apply: If you can generalize an action (i.e. "what would happen if everyone does this in this situation") without contradiction, then it is moral. Otherwise not.

What it cannot do is weigh two actions against each other: Lying is immoral, but so is treason. You might be forced to break one principle to protect the other.

Kant is kinda famous for taking extremist views in these circumstances.
He regarded lying as the worst kind of immorality. Which, with a bit of hindsight, leads to the questionable stance, that it is worse to lie to a nazi, than to protect and harbor a jew from death.
Obviously not a popular stance nowadays, and probably not even back then...

But you can fix that by applying a different 'order' to the individual principles. Modern kantian theories heavily focus on these parts.

I'm not sure if you can dismiss context entirely when thinking about a single action, I have the feeling that not. But on the other hand, I cannot think of an example where context does matter, but does not simultaniously pit two moral principles against each other... The answer to your first question kinda hinges on that...

About the loner part: Kant was among the most influentual figures in the european enlightenment movement, he wrote the very influental pamphlet "What is the enlightenment", and he regularly held lectures at various universities.
I dunno if he was an introvert, but he certainly didn't avoid society or discussions.

He was a racist, though. Even made money through questionable lectures on the inferiority of non white races. Not that uncommon (and widely accepted) in Germany at that time, but yeah... Great intellectual, an actual liberal in many ways, but still a shitty asshole in many others...

And for academic vs practical: Another name for the whole branch of moral philosophy is "practical philosophy".
It is not possible to make an actual useful distinction between academic and practical application of morality. The questions are the same, the reasoning is the same.
Only difference is if you have to actually go through with your choices, which makes it emotionally different, but not logically...

I'm a bit of a Kant fan, but here are some telling quotes from wikipedia: (Not all about his moral phlosophy thoguh)
"Kant's influence on Western thought has been profound."
"Kant is credited with having innovated the way philosophical inquiry has been carried at least up to the early nineteenth century"
"Arthur Schopenhauer was strongly influenced by Kant's transcendental idealism."
"With his Perpetual Peace: A Philosophical Sketch, Kant is considered to have foreshadowed many of the ideas that have come to form the democratic peace theory, one of the main controversies in political science"
"Jürgen Habermas and John Rawls are two significant political and moral philosophers whose work is strongly influenced by Kant's moral philosophy."
"Kant's influence also has extended to the social, behavioral, and physical sciences, as in the sociology of Max Weber, the psychology of Jean Piaget and Carl Gustav Jung,[199][200] and the linguistics of Noam Chomsky."
"Kant's work on mathematics and synthetic a priori knowledge is also cited by theoretical physicist Albert Einstein as an early influence on his intellectual development, but which he later criticised heavily and rejected."