1. If your uncle's sister is not your aunt, what relation is she to you?
Your uncle is either your mother's or father's brother. Any sister of your uncle would be your aunt, unless...

2. What gets wetter the more it dries?
It gets wetter, so the object isn't getting dry - it is causing something else to dry.

3. What word of only three syllables is composed of 26 letters?
Don't try to find a 26-letter word.

4. What is harder to catch the faster you run?
You are not trying to 'catch' something in your hands. This riddle is using an idiom.

5. What coat is always put on when it is wet?
In this case the 'coat' is not something you wear.