incorporated in my enthusiasm to contribute to this school,Does this make sense?

My yearning to develop skills and to become the best I can possibly be, will be

incorporated in my enthusiasm to contribute to this school.

Technically it makes sense, but it's a pretty rough way of saying it in my opinion. Maybe you could use the terms "My ambition" and "desire to improve myself" or something a little more smooth and compact.

You might try something like:
My quest for self-improvement and enthusiasm for skill development will be reflected in my contributions to this school.

They both make sense, but you might want to watch the flow of the sentence. You can always use a thesaurus to make sure you're using the exact right word to get across your meaning.

Hope this helped!

peachykeen sounds more standard, a reader will be confused at first though.. i dont know my two cent.

It sounds a bit confusing...
Try something like:

I will always strive to develop skills which will make me become the best I can be.

Usually concise sentences are more clear.

No! :-)

You could, maybe, incorporate enthusiasm into a mixture of emotions you are feeling right now.

Don't try to be too fancy. Have you ever read a book by Stephen King? He is not fancy so why is his writing so powerful? You should write the way you would speak if you were the most excellent communicator you can be. That means leading the reader's attention rather than encumbering it.