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well you can only send pictures in here, buts its hard. the way you can tell if its copper is it will look green in some areas and when you scape it with a knife it looks cooper or the color of a penny. So just take a old penny and a new penny and compare. IF its metal iron water pipe it will be magnetic and a magnet should stick to it. All a water softener does is remove the iron in the water , that is it, if you looking to clean the water then you filter it with different types of filters then go threw a softener. So a softener is very good for you and your pipes.
think what you want and read what you want do what you want, water with heavy calcium needs a filter , water with high iron still needs a filter . so thats up to you to decide how bad your water is and what you want to spend on a system. A good system is like 2-3000 installed. Also depends on what type of unit and manufacture , some softeners work different than others.
No soften water will not damage copper pipes, out of 100% people with soft water 80% of people have copper water pipes. water is under pressure in the pipe and little 2 no oxygen inside to react to the pipe, so in a sealed system then minerals don't bother the pipe. If you install a water softener it wont matter because it wont run if you already have soft water so its point less to get. What you would need in the case of high calcium is a hole house filter 2 part 1 part paper or fiber filter then into a carbon filter then into the house. these filters will remove the heavy minerals that you are asking about, if you don't believe me call a local water and perfection company and ask them.
Menard's has a hole hose filter that is about 300.00 they are nice and i have one in my home. it cleans itself once a day and never needs a filter to be replaced. its in the plumbing section and looks and is the size of a small softener but its a hole house filter. Also you can get ones like these www.home-water-purifiers-and-filters.com/whole-house-water-filters.php but Kenmore , sears , and culliagn all make similar models and cost about the same. they are easy to install but should be installed by a local plumber to insure proper installation and warranty