They can use Nokia brand only for few years, they don't have rights for it. It was known right from the beginning of this selling story that Nokia brand will disappear from mobile devices industry. Only the remaining parts of Nokia, not sold to Microsoft (part working on localization services etc.), will be able to continue to use this name.
Correct. But IIRC when acquisition was announced, they said that Microsoft would have license for using Nokia name only for Series 30/40 phones, so there would be Microsoft Ashas, Microsoft Lumias and Microsoft Nokias as 3 product lines. Later news media reported rumours about negotiations for additional licenses.