Check the DynamicSystems Package for controllability commands

Your first problem: yes, Maple is sometimes not intuitive.

Your second:

plot([[t^2,t,t=-1..1],[sin(t),cos(t),t=0..2*Pi]],scaling=constrained);

You need the implicitplot command:

restart:
f := 4*x-x*y^2 = 5;
g := (1/3)*x^3+y^2 = 1;
plots[implicitplot]([f, g], x = -10 .. 10, y = -10 .. 10,grid=[80,80],colour=[red,blue]);

If you leave the veggies out, you could overlay separate plots. Use plottools-disk, for example.