The reason the 唱歌 (Verb+object) would be in the subject position is of it was a passive sentence so here are two versions 我唱歌唱得好 I sing the song well 唱歌我唱得好 the song is sung well by me The passive sentence basically puts the focus on "something is done to something" rather than "somebody did something" the second sentence can also be written 唱歌被我唱得好。 The "被" is a particle that comes before the subject in the passive voice sentence

唱歌 = sing literally sing a song 歌唱 = the act of singing, literally "Song sung" 我唱歌[唱得]好 = I sing well. 我歌唱[得]好 = My singing is good. In your first sentence, if you put a comma or interjection, then it will make better sense. Punctuation marks in Chinese is an early 20th century addition when Chinese began to interact with western languages. 饭, 他做得好吃 = Rice (the act of making it), he does it well. (Just like in English creative writing)

通常我是說 ，他做的飯好吃 and 他唱歌唱得不好 Your grammar book is not so correct...

Okay, first of all I didn't learn Chinese the way you did, so bear with me, I'll just give you my own understanding of the sentence "唱歌他唱得不好". 唱歌 is indeed an object (a noun) 他 is indeed the subject (a noun as well) 唱 is indeed a verb 好 is indeed an adjective But I would have written it as "他唱歌唱得不好" (this is how I would normally say it as well 90% of the time). It is more direct, and clearer in my opinion.