1- to know the range of public IP addresses that your internet line have, call your provider. What type of internet connection you currently have?
2- As win32sux said, yes it is very important to update your system ( no mater what flavor of linux you running). The open source community constantly review the code and patch it.
3- If you want for a machine to use the DNS server then they both have to be on the same IP subnet or separated by a network router. If the IP address of the DNS server is different from your other then there should be a router between each network. All the websites internet services have different IP addresses but they still see each others via awesome devices called routers. i don't want to make complicated on you but it sounds to me that you need to learn a little on how IP addressing / subneting works. Usually that scars a lot of people but it's actually a lot of fun and very very extremely essential. here is a start http://www.learntosubnet.com/
and there are tons of documents on the internet on IP addressing and subneting.
What do you want your squid proxy server to do? do you want it to be an inbound proxy or outbound proxy? Squid is a big thing yet can be very simple and it's used by a lot of comercial products. We will be here if you have any more questions.