3. No. When making a PayPal payment, the customer has to login to PayPal to complete the transaction, so no need for Admins to have access to that. Though, you can "Login as client" to access PayPal payments.
5. Not with PayPal, Blesta does not store credit card expiration numbers when paid via PayPal, nor does it have access to any of that.
6. If the customer sets up a PayPal subscription, the payment will occur from PayPal automatically if they have enough funds.
If you want to accept credit card payments directly, you will need a merchant gateway like Payflow Pro, or Authorize.net. We are partnered with Evo to provide good discount rates to our customers who want to use Authorize.net. You can sign up at https://www.evopayments.us/accept-payments/blesta/ if you are interested in that.