If you want to use the word 'but', you can say, "There are but four books on the shelf. In this context, 'but' means 'only'.

I would say chirp, sing, or tweet are all common with 'sing' being the most common I should think, but like John V Hall explained, there are tonal differences between each word. As for the songs of the cicadas or grasshoppers, 'sing'.

These are common phrases, but not the way you've written them. Adrienne Salvi has written them in their common form.

They are all acceptable. "More or less" isn't so much about an adjective or adverb here as it is describing 'how much'. It's a qualifier. You can say, "I'll be there at noon more or less." or "Tony's a good guy more or less." The first example means that I'll be arriving at noon, but there's the possibility that I'll be there a little before or even a little after. The second example means that Tony is not a bad person, but there are perhaps some things about him that are not so good.

'Draw near' something means to get close to something. "When you draw near to my home, call me and I'll come right out." "Reflect off the moon" can mean to catch the moon's reflection or can mean to reflect the light of the moon. It's a little harder to answer the second question without more understanding of the story and this 'eye' thing.

All of your sentences were good.

It means, 'that at any time'