Step 1: Think about the parent acid and base
Strong base plus weak acid always gives an alkaline salt solution.
Step 2: Test each statement
Hydroxide ions increase, so (A) is true. The pH moves above $7$, so (B) fails. H$^+$ drops, so (C) fails. Blue litmus stays blue in base, so (D) fails.
Final Answer:
Option (A).
\[ \boxed{\text{(A)}} \]