Russia has no direct link to Königsberg, and in fact, it's much more profitable for Russia to sell this money sink to someone interested in paying for a prestigious object.
Not really. The last years have shown that Russian leadership still thinks in 19th or early 20th century terms regarding military usefullness of an area. Königsberg is a fleet base that can threaten the entire Baltic much better than St Petersburg which is at an end of a fairly narrow inlet.
Think in 1940 terms of aviation performance and army mobility and it suddenly makes sense. Ridiculous and outdated but there it is. In the same vein, Russian control of Crimea means that Russian land based aviation (of 1940 vintage) can control the Black Sea and its airspace, this is even how the Crimean invasion is sold to Russian public - somehow forgetting both the fact that modern (Russian or Western) naval warplanes have far larger range and that modern ground to air missiles started in Bulgaria can shoot down planes in Novorossijsk and the other way around.
As to including Königsberg/Kaliningrad as a bilingual state in the federation, besides the fact that Poles would have kittens at the time (and Kohl had to take wishes of USA/UK/France in account at the time, who in turn took Polish wishes seriously), the amount of German tax money to be sunk into rebuilding the impoverished, corrupt hellhole from the ground up... would be completely unpalatable to the German taxpayer without actual Germans in the area to be reunited with Germany proper.