Can I rely on my own DNS server in case of a global DNS blackout?

Having a cache of all DNS records is not feasible. Setting up your own root server on the other hand is! ICANN provides the root zone file here: http://www.internic.net/zones/root.zone

So just set up your own root server, point your DNS servers to it and you should not notice anything.

For Windows there was a program called Treewalkdns that acted as a personal caching dns server. It seems to have dropped out of site but it's probably available somewhere on the web.

There is a Linux program called PDNSD that addresses your requirements: http://members.home.nl/p.a.rombouts/pdnsd/index.html#aboutpdnsd

I can only answer your second question, sorry. Here goes:

It is possible to create a non-expiring cache of DNS records on a local machine by editing the hosts file. For example, you could add:

# Google
173.194.65.100 google.com www.google.com

To get the IP address to which a given domain name resolves, you could use ping or nslookup.

Rather than trying to set up your own root server, it'd probably be better to rely on Google's DNS servers for this:

http://code.google.com/speed/public-dns/

IPs:

• 8.8.8.8
• 8.8.4.4

It's likely that Google has a lot of DNS entries, and they definitely have enough processing power and bandwidth to have a very large DNS cache and survive constant polling from hundreds or thousands of users. My guess is that Google also isn't silly enough to let all their DNS entries expire if they can't contact the root servers.

You could also try connecting to OpenDNS. Maybe write the Google and OpenDNS IPs down somewhere anyway, so in case the root servers do indeed go down you have a few different options to try.

EDIT: Here is a more complete list of unofficial/alternate DNS root servers (on Wikipedia).