West Berlin was a military protectorate of the three western allies, however, it was included in the West German Grundgesetz as part of Germany. East Germany was also included in that constitution (along with Silesia and East Prussia). West-Berlin's Verfassung from 1950 (which also claimed jurisdiction over East-Berlin) also claimed Berlin was a Land (state) of the Federal Republic of Germany. The allies rejected this part of the Berlin constitution based on the four-power status of Berlin. Berlin was still an occupied territory under the ultimate control of the allies, but the western allies allowed for West Berlin to have its own parliament and Regierender Bügermeister (mayor of a city-state). The western allies also accepted that parts of the Grundgesetz could apply to Berlin, but Berlin's parliament voted on each federal law in order apply it to Berlin as well. Berlin elected representatives to send to the Bundestag in Bonn, but they couldn't vote on legislation. However, citizens of West Berlin were citizens of West Germany and could stand for federal election, which is how Willy Brandt was elected chancellor. West Germany also provided funds and subsidies for the economic development of West Berlin, since private investors weren't clamoring to invest in projects in a locale literally in the middle of a communist country.

There were all sorts of peculiarities about sovereignty in Berlin. For example, the U-Bahn service in West Berlin was administered by the western BVG, but the S-Bahn was run by the East German Reichsbahn. Even after the Four-Power agreement on Berlin (in which the word 'Berlin' is never used, rather 'relevant area') the status of Berlin really still depended on who you asked.

Berlin (West) as it was known was de jure part of the FRG, with certain provisos. The Western Allies (the US, the UK and France) said that while the occupation of most of Germany had ended, the occupation of Berlin had not, and thus the occupying powers were therefore still the ultimate authorities in Berlin (the occupation of the city could only be ended by an agreement of all 4 allies and that was not politically tenable until the end of the Cold War).

Parts of the Basic Law of the FRG didn't entirely apply to Berlin as an occupied state--the basic guarantees in articles 1-3 (of the inviolability of human dignity, freedom of the person and of equality before the law) were only applicable insofar as the commanders of the occupying powers allowed it. Residents weren't allowed to vote in federal elections (although they could stand for election; Willy Brandt, an FRG chancellor, was a Berliner).

Laws passed by the Bundestag were not automatically extended to Berlin. Berlin was represented in the FRG government by nonvoting delegates. However, the city council-equivalent (the Berlin Senate) as a matter of course passed all laws passed by the Bundestag to keep Berlin on a legal equivalent with the rest of the FRG. Because of the Allied veto over all the laws, though, residents were exempt from military service in the Bundeswehr after the commanders vetoed that bill.

The administrator of the city was the Governing Mayor and the previously mentioned Berlin Senate, with the commanders of the Western allies exercising veto power.

I hope this answers your questions!