I have a approved vendor. How do another user be added into the system under this vendor. Can the vendor have the privilege to add another user ?

Hi,

You need to enable Apply for a vendor form. You can do it in Admin panel -> Configuration -> Settings -> Vendor settings - and mark the Allow customers to apply for vendor account checkbox. After that, after successful customer registration, every customer will be able to register as a vendor in your store.

That all looks good. But after a customer apply for vendor account, why do I have to add the customer a vendor role after I activate the vendor. Ideally, when I activate the vendor, the customer who applied for vendor account should also be automatically given the vendor role. Why should I again  have to set vendor role for that customer?

Well, it's a current architecture. We are thinking about it's improvement, so we will be glad for each suggestion. You can report them here.