I am new and I am catching onto the knowledge slowly.

I have a:
coinbase account with public key(I can't find a private key)
blockchain account with public key(I can't find a private key)
paper wallet with public and private key.

1st I thought you needed a private key to send money....why doesn't coinbase or blockchain have a private key?
2nd I want to move my paper wallet into my blockchain account so I can spend it.  If I import my key do I retain complete control over that money still?  ie. If blockchain goes bankrupt am I still in control over those monies b/c I imported vs sweeping?

Thanks.