1. Can I use a 19-26 mm tube for a 28 mm tire [700 mm, Specialized Road Armadillo]?
Yes, but ideally get the proper size. The rubber is stretched thinner and may be strained round the valve (pump up a tube out of the tyre, and you'll see the diameter increases least at the valve).
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2. If my tubes never get damaged, should I still replace them on a periodic basis? How frequently?
I would say every year or two. Eventually they fail at the valve, where they can't be patched.