Not quite. There is a grammar problem in the middle of the sentence. You can't say 'if it's possible that you waive'. One way of correcting it would be this: "I'm writing to inquire whether it's possible for you to waive the registration fees for us" Now it's correct, but still informal. Two ways of making a request sound more formal and more polite are to remove the contractions and to make the sentence a conditional, for example: "I am writing to inquire whether it would be possible for you waive our registration fees"

Sounds good! Instead of "if it's possible that you waive" I would write "if it would be possible for you to waive," but it's a subtle difference.

It's not bad, but would be better a little simpler: "I'm writing to ask if it's possible for you to waive our registration fee" :) 'inquire' is a little harder to use; 'inquire as to whether you could.."

I believe there is nothing wrong with thay, and it's polite and formal. :)