dig doesn't use the local nameserver unless you're looking up a name there: it queries remote nameservers directly.
No it does not. By default, dig uses the nameservers in resolv.conf. Check your dig output sometime.
Performed on a box where resolv.conf points to 127.0.0.1:
$dig www.news.com <snip> ;; Query time: 201 msec ;; SERVER: 127.0.0.1#53(127.0.0.1) ;; WHEN: Tue Dec 14 18:55:54 2004 ;; MSG SIZE rcvd: 138
Dig queries servers directly if you use dig @<serverip>, but otherwise it queryies the servers in resolv.conf.