Short answers, pulled from the story.
Mozart traveled to Berlin in spring 1789 primarily to seek concert income and royal commissions during a period of financial difficulty. He was no longer earning much from concerts and had been borrowing money from friends such as Michael Puchberg. He traveled free of charge by accompanying his patron Prince Karl Lichnowsky, who had his own reasons for visiting Berlin.
Mozart traveled with Prince Karl Lichnowsky, an aristocratic patron and fellow Freemason who was also a patron of Beethoven. Lichnowsky offered Mozart free passage. The singer Josepha Duschek also traveled independently through several of the same cities, including Dresden and Leipzig, and performed alongside Mozart.
Mozart arrived in Potsdam on the 25th of April, 1789, but received no royal welcome. A court document recorded his presence in bureaucratic terms, and the King's response was to direct him to Jean-Pierre Duport, director of the royal chamber music. No audience was granted at that time, and there is no solid evidence that Mozart even remained in Potsdam during the weeks that followed.
Mozart improvised on the organ of the Thomaskirche, where Johann Sebastian Bach had previously served as music director. The cantor Friedrich Doles, a pupil of Bach, and organist Karl Friedrich Gorner worked the stops for him. The choir of the Thomasschule performed Bach's motet Singet dem Herrn ein neues Lied, BWV 225, and Mozart copied the entire composition out from all the separate choral parts.
After performing before Friedrich Wilhelm II and the Queen at the royal palace on the 26th of May, 1789, Mozart received 100 Friedrichs d'or (around 800 florins) and commissions for six string quartets and a set of six easy piano sonatas for Princess Friederike.
Yes. After the journey it emerged that Mozart owed Lichnowsky 1,415 florins, possibly incurred during the trip itself. Lichnowsky pursued the debt legally and won a judgment against Mozart in October 1791, shortly before Mozart's death.