Value of constants in Big Theta notation
No, the constants $c_1,c_2$ are the same for all values of $n$. If they could depend on $n$ then the definition would be meaningless since $\Theta(g(n))$ would contain all positive functions. Indeed, suppose $f,g$ are two positive functions. Then for all $n$, $$c_1g(n) \leq f(n) \leq c_2g(n) \text{ for } c_1 = c_2 = \frac{f(n)}{g(n)}.$$