How can solve this riddle? (See comments)

This hurts my brain right now but I won't google it cos I won't. Something with eat or apple in in it , eat is in it !!! For sure , maybe, I'm answering because I wanna know the answer and so I can find my way back :p

I am word with six letters.
My motto is together as one.
If you remove my first and second letters, you can wear me.
If you remove my third letter I can be painful.
If you remove my second, third and sixth letters, Adam & Eve did it.
If you remove my second and third letters, you do this using your mouth.
What am I?

i got to about the third sentence and my brain went into a full system shutdown sorry i tried