Consider a particular representation of $\operatorname{SO}(2,\mathbb{R})$: \begin{equation} \begin{pmatrix} \operatorname{cos}(\theta) & \operatorname{sin}(\theta) \\ -\operatorname{sin}(\theta) & \operatorname{cos}(\theta) \end{pmatrix}. \end{equation}
We may construct new representations of a group by direct summing old ones. Consider the matrices
\begin{equation} \bigoplus_{j=1}^n \begin{pmatrix} \operatorname{cos}(\theta) & \operatorname{sin}(\theta) \\ -\operatorname{sin}(\theta) & \operatorname{cos}(\theta) \end{pmatrix}, \end{equation}
\begin{equation} \bigoplus_{j=1}^n \begin{pmatrix} \operatorname{cos}(\theta_j) & \operatorname{sin}(\theta_j) \\ -\operatorname{sin}(\theta_j) & \operatorname{cos}(\theta_j) \end{pmatrix}. \end{equation}
Do the examples provide a representation for any of these groups: $\operatorname{SO}(2,\mathbb{R})$, $\operatorname{SO}(2n,\mathbb{R})$, $\bigoplus_j^n \operatorname{SO}(2,\mathbb{R})$?
It should be clear that the direct sum of two representations $V$ and $W$ of a group $G$ gives a representation of $G$ on $V \oplus W$ by $g \cdot (v, w) = (g \cdot v, g \cdot w)$. Note that the matrix of $g$ on $V \oplus W$ is block diagonal, with the matrix of $g$ on $V$ in the upper-left-hand corner and the matrix of $g$ on $W$ in the lower-right-hand corner.
For the other questions, note that to specify a representation of a group it's not enough to list some matrices; you have to specify which group element corresponds to which matrix.