Yes, he killed those people. None of the themes work unless he killed those people.
The story is a criticism of yuppie culture. Yuppies have a lot of things, but one thing they don't have is individuality. Patrick is able to get away with his crimes (but unable, in the end, to get "credit" for them) because neither he nor any of his victims have any identity. He kills nameless hookers and homeless men, but this is not satisfying and soon feels the need to move onto something that might get him caught... or so he thought. Soon we learn that the concept of an alibi is meaningless when none of Paul Allen's friends and associates can even tell him apart from others like him. The characters constantly call each other by the wrong names; no one knows who anyone is and no one cares. This is the real condemnation of the yuppie culture: no one in it has any meaningful human relationship with anyone else, and no one is truly loved or cared about, and no one sticks out from the crowd even when they want to.
The lawyer did not have lunch with Paul Allen in London. He only thinks he did. He had lunch with some other guy in a suit he thought was Paul Allen. He doesn't know Bateman's face, and he doesn't know Allen's face. And even when people suspect a crime took place (the real estate lady at Allen's apartment, Bateman's lawyer), they ignore it and sweep it under a rug. They don't care about anyone else enough to get involved in a murder investigation. When the real estate lady saw corpses piled up in one of her properties, all she was was lowered property value. When the lawyer heard his client's grisly confession, all he heard was a client who hadn't been caught running his mouth unnecessarily. That's why he excused himself.
Not that either of them care at all about Paul Allen or Patrick Bateman, or even know who they are. As Patrick puts it himself: "I'm simply not there."
