Some of these are definitely the normal phrase - so I won't mention those again - but they are correct.
13. The normal phrase for a dog is actually 'bark', not 'barking'.
It is the same for other sounds, as
thar says; 'a yip' not 'yipping'.
The '-ing' versions are used for a more continuous or general noise.
His dog's bark alerted him to an intruder.
The barking of the dogs in the courtyard alerted him to an intruder. You could also use 'howl', 'howling' or 'racket' - depending on what it actually sounded like to you.
16. I've also never heard a beetle click. The only sound I've heard from a beetle is a 'whir' or 'buzz' (as they fly into a lighted room from the dark) and a 'thump', 'thud' or 'whack' (when they crash into the wall or window).
18. Wind in grass is usually said to 'sigh'. But that's not on your list.
If the grass is dry, it might 'rustle'. 'Murmur' may fit too.
19. A normal electric fan may 'whir'.
An unbalanced or broken one may rattle.
21. You don't normally hear a bullet flying really. I believe that a bullet may 'whir' or 'scream' after it has ricocheted and slowed down and is tumbling.
When it hits something, the sound depends on what it hits - 'splat' or 'whack' are the only ones on your list that I might use.
22. As
thar says, it depends. Other possibilities (one's I've read or would not be surprised to see) are:
Rumble, racket, scream, howl.
24. Yes - the usual phrases would be "the song of a nightingale" and "the coo of a pigeon or dove".
None of the supplied words really fits that one.
26. Like aeroplanes and fans, motors have
many sounds. It depends on power-source and size.
27. A window in the wind (if it is not fitted perfectly) rattles.
28. I haven't heard a tea-kettle whistle (or 'scream', some people may say) in many years.
However,
thar is right. That's what was the expected answer.
Wyrd bið ful aræd - bull!