It's not easy to digest this movie if you haven't seen other Tarkovsky works prior to Stalker. It's possibly his most personal movie. You got most of the plot right, but you shouldn't take a necessarilly literal interpretation of it. It's an allegory, symbolic.
Here's an excerpt of my review where I express my, also uncertain, reading of the movie:
"Not easy to fully dissect what a first view unravels but I'll say it seemed to me an essay/allegory about faith, about the eternal search for the Truth and about the way how different thought paradigms deal with the task. I liked the way how this last point was worked out. 3 characters: "Stalker", the one who guides the other 2 through "The Zone" seems to represent the religious or moral paradigm, the "Writer", the Art paradigm and the "Professor" represents Science. Each character, ie, each paradigm has it's own point of view and it's own reason to search for the Truth, the way how their interaction was developed seemed well judged and congruent to me. At the edge of the room where the Truth is to be finaly consumated, the 3 paradigms start fighting between each other and with their own reasons, naturally no one goes into the room because the Truth can only be aimed at from a distance, we still cannot touch it."
I must say this movie is highly fascinating to me, but I understand why you find it cold and depressing. Tarkovsky wasn't concerned about making acessible or pleasing movies, he is highly intellectual, that's part of the reason why his Cinema is so singular.
Here's an excerpt of my review where I express my, also uncertain, reading of the movie:
"Not easy to fully dissect what a first view unravels but I'll say it seemed to me an essay/allegory about faith, about the eternal search for the Truth and about the way how different thought paradigms deal with the task. I liked the way how this last point was worked out. 3 characters: "Stalker", the one who guides the other 2 through "The Zone" seems to represent the religious or moral paradigm, the "Writer", the Art paradigm and the "Professor" represents Science. Each character, ie, each paradigm has it's own point of view and it's own reason to search for the Truth, the way how their interaction was developed seemed well judged and congruent to me. At the edge of the room where the Truth is to be finaly consumated, the 3 paradigms start fighting between each other and with their own reasons, naturally no one goes into the room because the Truth can only be aimed at from a distance, we still cannot touch it."
I must say this movie is highly fascinating to me, but I understand why you find it cold and depressing. Tarkovsky wasn't concerned about making acessible or pleasing movies, he is highly intellectual, that's part of the reason why his Cinema is so singular.
HIs cinema is so singular in the sense that he is the only (major one at least) art filmmaker that represents classical art applied to cinema. Nothing else in terms of movies feels more like 18th-19th century classical and Romantic music or feels like a Russian novel from the 19th century than Tarkovsky's films.
His films feel inaccessible because they are Russian, very, very, very Russian. It's a very different flavor from the American flavor of most movies that we all watch, but it's not something that is inacessible for the Russian public: in 1979, Stalker sold 4.3 million tickets in the USSR. That's 6 times more than Miyazaki's Castle in the Sky sold in 1986.