15. Was the famous Broadwood piano Beethoven's favorite?

No. He got his Broadwood in 1818 when he was already very deaf, too deaf to judge the instrument objectively. However, he appreciated the precious gift, ordered by some of his best Viennese friends and sent to him by the London manufacturers. From about 1810 he had had troubles with finding a good substitute piano, after he had given up his many attempts to improve the Erard he had received from the French manufacturers in about 1803. He tried one piano after another in the period 1810-1817 and finally he got the famous Broadwood, which surely is an impressive piano indeed. He was grateful, of course. And he was told that it was an excellent instrument. That's the background of his so-called appreciation of this particular instrument. But what we know about his likes and dislikes of pianos points to Viennese instruments (Walter, Streicher), not to English, nor to French.

Newman, W.S. Beethoven on Beethoven. Playing his piano music his way. (New York/London, 1988).
Skowroneck, Tilman. Beethoven's Erard piano: its influence on his compositions and on Viennese fortepiano building. In: Early Music (2002).