All these points put me on the idea that PayPal offer air to their customers, not Bitcoin. No private keys, no deposits, can't sending - they offer a nothing. Do PayPal have information on how their cryptocurrency will be backed and what evidence they can provide? It seems to me that you shouldn't deal with them.
Yes, they trade only air or as say - artificial bitcoin. Also trading Bitcoin on paypal
might cause your account to be blocked. Paypal can also freeze your funds for 10-14 days for suspicious action (even receiving $30 can be a suspicious action. I have my funds frozen for 2 weeks without any reasonable explanation).
If you have issues with Paypal, get ready to be answered with default answers from FAQ and support not interested in solving your case. Dont forget that you might wait for days before Paypal support even answers you, as it seems they are lack of employees in support.