Actually, believe it or not, the physical conditions on the surface of the star are not determined by nuclear burning. In fact, we had a fairly good idea of the structure of the sun before we even knew about nuclear burning. The majority of a star's structure is determined by battle between pressure and gravity. The thing determined by fusion is how long it can maintain this equilibrium. The star is cooling via the light it emits, so the fusion is needed to keep the temperature up and maintain the pressure. In other words, the energy source determines the lifetime, not the structure or appearance.
Metals have two effects. First, their absence or presence will alter the radiative opacity of the atmosphere. This will, in turn, alter the luminosity. Specifically, metals tend to make the atmospheres more opaque, decreasing the luminosity. Thus, metal-poor stars (subdwarfs) are dimmer. The other effect of metals is to alter the spectrum and, therefore, the color. Metals contribute a lot of absorption lines/bands/edges, so a star of equivalent luminosity and temperature will have a different color if it has fewer metals.
The envelopes of stars expand into giants expand because their cores contract (conservation of energy). Their cores contract because they can no longer support themselves with nuclear reactions, so they collapse until degeneracy pressure kicks in. If the star is massive enough, it will eventually start burning helium and the core will expand again, allowing the star to shrink back to a more reasonable size.
