Water is complex in terms of coffee, and the answer is "it depends" in terms of how it will affect your coffee. Every coffee roaster tastes their coffee with a certain water, and it's likely the coffee tastes best with the water it was roasted against. You might experience the opposite problem from what you described with some roasts.
There are multiple things you'll want to account for. There are many undesirable flavors you can get from heavy metals, or chlorine-tasting water (so at a minimum you want your water to taste good). Beyond that, you really care about the amount of Calcium, Magnesium, and buffer (generally HCO3) in your water.
Based on what you said of your water, I suspect you have quite a bit more bi-carbonate hardness (HCO3 or buffer) in your water. This kind of hardness will rip out the acids in the coffee very well, but will also push the pH level of the final cup to a balanced state. Your friend's water likely lacks enough to bring the coffee's pH to a balanced state where it's enjoyable (fun hack, add ~2g/L of baking soda to water, a source of bi-carbonate, and add this in increments to the final coffee, you can fix the acidity!)
Calcium and Magnesium also work together to bring out acids and other taste-y bits to your coffee. Calcium + Bi-carbonate is why your kettle is scaling quickly. You can filter your water (a cheap Brita filter will remove Ca and Mg from your water).
I personally mix my water up from distilled for brewing to a specific ppm of Ca, Mg, and Bi-carbonate.
You can increase your total hardness of water if you get a better system by simply adding baking soda to the water, or other mineral salts. I would be careful about this however and ensure you are still creating something that is safe to drink.
If you want measure your water, you can use various titration kits to quantify your house water. If you want to do more research on water and coffee, this is the popular book on it. It's very hard to find, I got lucky enough to pick up a copy.
Hope this helps.