Answer:
What can you catch but not throw?
I fly to any foreign parts assisted by my spreading wings. My body holds an hundred hearts Nay I will tell you stranger things when I am not in haste I ride and then I mend my pace anon.
I am partially baked. I am not completely lit. I am a portion of the moon. I am lesser than full wit. I am a divider of the hour. I am not a total lie. I am a sibling through one parent.
If you have me, you want to share me. Once you share me, you won't have me. What am I?
Four leaves I have.
What do you purposefully put lots of in and on your body, but run away from when you encounter it outside?