Grammar/meaning of 好 in ”怎么才能唱好歌?“ ？ I came across this sentence and I assume the meaning is "how can I (learn to) sing well?". What I don't fully understand is the grammar of 唱好歌.

I know that 好 can be used as a result complement like 我做好作业了 I've finished my homework. The meaning I've learned for 好 when used this way is "finished to a satisfactory standard".

I assume that 唱好歌 is simply 唱歌 with 好 inserted in the middle because 唱 is the verb and 歌 is the object.

My first question is - is this the normal grammar for asking this type of question, or is there an alternative structure? For example, if I want to ask how can I (learn to) cook well, is 我怎么才能做好饭 correct? 

Second question - does the above sentence carry a meaning of "how can I cook (this specific meal) well" or "how can I generally cook well"? Or can it be either depending on context?

Third question - I've learned that I can insert 得 or 不 between a verb and complement to make a potential complement structure. Therefore, if I want to say "I can't sing well" is it 我唱不好歌? If not, why not? If yes, what's the difference between this and 我唱歌长得不好?

Thanks very much in advance to anyone who can help!
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.