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I suppose it depends what the filter is actually filtering. Very hard water requires quite specific filtering to be really good for coffee machines. Might be worth getting a test kit (from BWT or similar) and seeing what goes in Vs what comes out, however I'd prefer to have the water treated before it hits the machine at all.
Some people use mineral waters, some people filter their mains and use that.
Yes, depending on how the machine is fed, is it a tank you fill manually or mains connected?