I don't think Filtered water would necessarily make a better beer. It all depends on what kind of tap water you have. A lot of tap water is great and can make great unique beer. It also depends on what type of beer you are making. Different water profiles are better for different types of beer.
I've used different types of spring water and tap water and I haven't noticed a difference. Unless you want to start building your own water, if it tastes fine then use it.
depends on where you live. A lot of breweries just use tap water (Anchor for one)...Best is to get a water report, but you shouldn't worry about it. I think the rule of thumbs is if it looks good and tatses good it will make good beer.