java.io.NotSerializableException: org.jboss.weld.bean.ManagedBean
This is a bug in Mojarra. It has been reported as issue 3191. It's fixed in Mojarra 2.2.7 whose release is expected 3 july 2014. If you need to get it fixed right now, grab the 2.2.7 snapshot. See for download details the answer on How to download Mojarra JSF nightly builds.
Also it is Java EE 7 though the IDE (NetBeans 8.0) issues a warning,
Unsatisfied dependency: no bean matches the injection point
Sorry, Netbeans is beyond me. If you're already using the latest Netbeans version and you are confident that Netbeans is Wrong (i.e. everything just works apart from the particular exception), then you'd report an issue to them.
In Java EE 7, there should not be a need to create the beans.xml file. So, this warning should not be issued.
You're completely right. See also this blog of Reza Rahman: Default CDI enablement in Java EE 7.