Finding running time
Instead of solving the question for you, let me show you what steps you need to take in order to solve this problem on your own.

Suppose that $T(1) = T_0$ and $T(2n) = C T(n)$ for all $n$.


What is $T(2)$? What is $T(4)$? What is $T(8)$? What is $T(2^k)$?


Now suppose that $T$ is monotone: $T(n_1) \leq T(n_2)$ whenever $n_1 \leq n_2$.


If $2^k \leq n \leq 2^{k+1}$, what can you say about $T(n)$?
Can you now deduce the asymptotic rate of growth of $T(n)$ for arbitrary $n$?