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To answer your second question:

sage: f(x) = x^2+5
sage: g(x) = 25*sqrt(x+1)
sage: g(f(x))
25*sqrt(x^2 + 6)
sage: f(g(x))
625*x + 630
sage: h(x) = f(g(x))
sage: h
x |--> 625*x + 630

The first one is harder, because Piecewise functions were implemented long before we even had symbolic functions, and hence are missing a lot of functionality. This is a long-standing need, but it takes a certain expertise in both the old and new code, as well as Ginac, to do this.

(To the cognoscenti - sympy seems to have piecewise functions, but I can't find much documentation, just obscure hints that they are there. How powerful are theirs?)