Definitely. Although there is no such thing as perfect security, a properly configured Linux, *BSD or Unix system can be very secure and orders of magnitude better than any version of windows.
Linux, Unix and *BSD are 100% immune to windows viruses and exploits as long as you don't install WINE ( WINE allows windows software to run on Linux ). There are about 80,000-100,000 windows viruses, while Linux only has about 100, MacOS X 60-100 and Unix about 10-100.
If you use well written firewall rules, SELinux and you configure and use the system properly it can be very hard for anyone to break your security.
Some security experts recommend using only one computer or a secure Virtual Machine (VM) running on top of Linux for your banking and ebay and nothing else. If you use your computer or VM for other tasks you'll open yourself up to a number of threats even if you have a very secure operating system like Linux.
Firefox is also more secure than other browsers, especially internet explorer, although firefox has been targeted due to its popularity.
Tell us about your hardware and what you're trying to do and the OSS experts on the forums will make some suggestions.
I will do a format this weekend and load vista, steam, drivers and block all ports except steam. I have chosen linux mint to dual boot as it's noob friendly, configure firewall rules, install avast for linux which is free for a year and install rest of the applications.
apt-get install clamav* or something like that should install it on debian based linux distributions like ubuntu and mint.
Linux supports whole disk encryption which can help keep your system secure. Since you are planning to dual boot whole disk encryption would certainly help, without encryption windows will be able to read and write to your Linux partitions and break your security.
If you use encryption use a good passphrase and don't forget it, if you write it down lock it up in a fireproof safe. You should encrypt all filesystems except /boot.
Not really. The issue is that you have a writeable file format right there for the bad guys to work with. I don't rate the main distros for live CD use, they are designed to be installed. Better in my eyes to use something designed to be live from the start.
The trick with many of the small 'mini distros' is to use the 'toram' boot option which leaves the whole CD loaded into RAM and makes it run like the proverbial off a stick. I've played with Puppy and Slax this way and if you've got more than a couple of gig of ram it's a whole world of joy.