I love that movie! But I haven't seen it in awhile. I must find it and watch it again.
The "subject" is Carol's (Helen Hunt) absence from work. Melvin (Jack Nicholson), has a disorder which forces him to live a life which is full of routines. He must tap his toes on the ground before putting on his slippers. He must lock his door in a very specific way. He must wash his hands with a fresh bar of soap every time AND he must be served breakfast by Carol while sitting in the same seat, every day.
As you remember, their were strangers seating in his seat when he showed up at the restaurant, and Carol wasn't there either. This was very very upsetting for Melvin. Melvin believes that his routine should never be broken, because if it is then his life will fall apart. His "routine", that is the subject which he is referring to.
In regards to your other question, Melvin's life is controlled by his own logic and rules. He has enormous difficulty trying to empathize with other people (until the end of the movie). From Melvin's perspective everything must proceed in a logical order. Carol has a job at the diner, and she should show up for work at the same time every day. She must never be absent from work! That's just logical. You have a job, you must show up to work. Melvin isn't (yet) capable of acknowledging other people's problems and he tries to keep emotions under control. Well, at least his 'kinder' emotions. When Carol doesn't show up for work he is very upset and angry but he immediately tries to control that. Remember that 'emotions' are a very dangerous thing for Melvin. I think Melvin knows deep down that he is being a creepy person by showing up at Carol's home, but he tries to cover that up by telling himself "It's perfectly logical for me to ask her why she is not at work. I'm not being creepy or strange, I just want to know why she is absent."
Melvin is full of crap of course, but he doesn't realize it until the end of the film.