Correct answers are

(a) $\quad \overrightarrow{V_{OS}} = \omega R \hat{i} \qquad \qquad \overrightarrow{a_{OS}} = \alpha R \hat{i}$

$\qquad \overrightarrow{V_{AS}} = \omega R (\hat{i} + \hat{j}) \qquad \qquad \overrightarrow{a_{AS}} = (\alpha + \omega^2) R \hat{i} + \alpha R \hat{j}$

$\qquad \overrightarrow{V_{PS}} = 0 \qquad \qquad \overrightarrow{a_{PS}} = \omega^2 R \hat{j}$

(b) $\quad \overrightarrow{V_{AB}} = 2 \omega R \hat{j} \qquad \qquad \overrightarrow{a_{AB}} = 2R (\omega^2 \hat{i} + \alpha \hat{j})$