As far as I know, any college or university- incuding top schools- would like a music supplement if it shows real talent and ability to contribute on campus, and helps them to get to know you. However, conventional wisdom is that you want to make sure that the level of your singing or composing justifies sending a supplement or it can backfire a bit.
I can’t really respond concerning the singing. Perhaps someone else will come along.
For composition, it is definitely better to write something of your own but if you say that you find it hard to “develop and sustain a musical theme”, it might be counterproductive to include composition in your supplement. I could be wrong: maybe you could write a little more about your experience, the style you compose in and so on.
Composing is not always about developing a theme 
Are you familiar with much 20th and 21st century composition? Meaning modern and contemporary concert/ “classical” music, often called “new music”? Or are you more into jazz or popular music?
If you are into classical work, then a goal would be to develop an individual style, eventually. An “individual voice.”
So it is fine if you decide to do a music supplement, but get some advice on the actual choral work or compositions that you want to submit. It is also okay NOT to submit a supplement and make sure that the common application reflects your involvement in and love of music. You can also put this in the extra information section.
If you do do a supplement, you can also include a music resume, list of performances, and letters of recommendation from music teachers and directors- but only if the submission is justified by the level of your work.
Hope this helps.