Grammar/meaning of 好 in ”怎么才能唱好歌?“ ？
I think, for Western ears, 怎么才能唱好歌 is ambiguous, whereas, for Chinese ears, it just means 'How can I sing well?'

Does it mean 'sing a good song', or 'sing well'? I asked a Chinese friend, she immediately said, "All songs are good." 

You could write 怎么才能把歌唱（得）好。

Q1 Yes, fairly normal grammar
Q2 我怎么才能做好饭 How can I learn to / cook well / be a good cook.

For a specific dish: 我怎么才能做好[name of dish]

Q3 我唱歌唱得不好。 or 我不会唱歌。

Do you remember an old song, 'Killing me softly'? In that song, it says, "I heard he sang a good song." There is no sense in this that he only sings one song well. 

It means 'He sings well.' 他唱歌唱得很好。

Similarly, 'She bakes a mean cake.' says: 'She bakes well.' not: her cake is somehow unpleasant.