They are able to burn. Companies doesn't make DVD-ROM drives anymore.
About the IdeaPad Z510.
You can buy it on amazon. I didn't find it ether on the English version of Lenovos homepage.
However i found it in the danish version... that's odd.
Bærbar Lenovo Z510-computer | 15,6" bærbar multimediecomputer | Lenovo (DK)
Btw about the tech support. I think the one you have heard that from just had a bad experience with the support he was getting