Would you think they would release the private key to me?
I doubt so.
They'll probably take the free money and won't release any private keys to you.
But it still would be worth a try. They might be refunding it (for a fee).
So are these funds sitting in that wallet address or still on the block chain?
Bitcoins are ALWAYS 'on the blockchain'. They are NEVER 'inside' of a wallet or 'in' an address.
The blockchain is the public ledger. The BTC's are
assigned to an address.
And in order to use these UTXO's you'll need to have the corresponding private key to create a (valid) signed transaction.
Anyone with access to a private key, has access to all UTXO's associated to the addresses derived by this private key.
If they want to help me are they capable of sending funds back? Or how would they help me in this case
Yes.
If they want to help you, they are simply going to send the funds back. But i woulnd't expect them to do that.
Did you already find out why the first transaction got forwarded to coinbase ? This still seems to be somehow inconsistent because it doesn't make sense.