Question: How did Soze end up in the police station after he escaped the boat in the first place? If he had vanished after the bombing, he wouldn't have to make up the stories and he wouldn't have been identified by Kujan.
Answer: Kint/Soze ended up in the police station because he simply didn't get away in time.
Answer: Soze ended up back under arrest and for some questioning as 'Verbal Kint'. He never really vanished, he's just playing two parts/people. He really vanishes off the scene by the end of the movie after he tricks Kujan.
With the exception of what's known to have happened on the dock, the entire story is a lie told by Verbal Kint to Agent Kujon. Kujon realises this after Kint leaves the office but not in time to catch up. The entire movie is about a habitual liar making up a story about what happened on the dock. He may be Keyser Soze or an alter-ego variant but even Keysers rep is subject to question as it was told by the same liar. Verbal himself said about Keaton, "He was a grounded guy, a cop. If you think the husband did it then you're right." He was telling on himself as sociopaths will do when they think they're smarter than everyone around them.
Answer: All he had to do was kill them on the ship, blow it up, and leave. The whole BS story with the cops didn't even have to happen.