Can I pop my own cherry?

If you mean "tearing your hymen", yes, you can. The hymen is just a rather fine/fragile rim of tissue (membrane) at the entrance of the vagina.
If you mean "losing your virginity", for that you will absolutely need a mans' penis.
Not all girls bleed the first time they have sex. If they bleed it's often only a stain, no hemorrhage like your period. Lots of virgin girls don't have much left of their hymen at their puberty, due to a "tom boy youth": jumping, horse riding, gym (or just by using tampons)
My wife just spotted a bit. She was 20 then.

there's nothing embarrassing about a little bleeding when you lose your virginity... it actually added to a pretty funny story for my first time :)

Yes. I lost mine dancing. I use to be on a dance team and it "popped"

sure you can, it may be hard though.
but trust me, when the guy KNOWS he's ur first, he won't mind at all.
its kind of an "honor" for guys. its special, to both of you.

Yes, it is possible. Anything from riding a bike to masturbating can.