Boiling water remains the most effective way of clearing the water of microorganisms (better than any filter), but does nothing for nonbiological contaminants.
Ideally, you do both. Personally, I'm comfortable with just the filter. In hundreds of trips into the wilderness, the only time I've suffered from contaminated water (giardia -- don't recommend) was when I accidentally drank some unfiltered water. Fortunately, I didn't develop any symptoms until I was back from the trip.
Not really directly. You can buy old school, bootleg alcohol looking distiller systems for not much money. All it needs is a heat source, whether from a car battery or a small fire.
Ideally, you do both. Personally, I'm comfortable with just the filter. In hundreds of trips into the wilderness, the only time I've suffered from contaminated water (giardia -- don't recommend) was when I accidentally drank some unfiltered water. Fortunately, I didn't develop any symptoms until I was back from the trip.