Clarifying statements involving asymptotic notations in soln of $T(n) = 3T(\lfloor n/4 \rfloor) + \Theta(n^2)$ using recursion tree and substitution
&quot;$O(n^2)$ is indeed an upper bound for the recurrence&quot; means $T(n) \in O(n^2)$.
That is, $\exists n_0 \ge 1, c&gt;0, \forall n \ge n_0, T(n) \le c n^2$.

&quot;$\Omega(n^2)$ must be a lower bound for the recurrence&quot; means $T(n) \in \Omega(n^2)$. That is $\exists n_0 \ge 1, c&gt;0, \forall n \ge n_0, T(n) \ge c n^2$.

This is exactly the same as 1).

Yes. In this step you use induction to show that $T(n) \le d n^2$ for some choice of a constant $d &gt; 0$.