Only option C is correct. It is a direct application of Demorgan's law.
$\sim (p\vee \sim q)=\sim p\wedge \sim (\sim q)=\sim p\wedge q$

p: 2 plus 3 is 5
q: Delhi is the capital of India
~p: it is not that 2 plus 3 is five.
Then the given statement is $q\wedge \sim por\sim p\wedge q$

p: It is snowing
q: I am cold
~q: It is not that I am cold

Then the given statement is $p\wedge \sim q$

A logical statement is a statement which has a definite truth value which is invariant. Here the statement 'you are a boy' depends on who 'you' are. Hence, it is not invariant.

$S(p,q,r)=\sim p\vee \sim (q\vee r)S(p,q,r)=\sim (\sim p)\vee \sim (\sim q\vee \sim r)=p\vee \sim (\sim (q\wedge r\left)\right)=p\vee (q\wedge r)$

p: Roses are red
q: The sun is a star
~p: Roses are not red
$\sim p\vee q$: Roses are not red or the sun is a star

p: 2+3 =5
q: 8 is less than 10
$p\wedge q=\sim p\vee \sim q$
$\sim p\vee \sim q:2+3\ne 5or\text{8 is not less than 10}$

The sentence I have failed can have different truth values depending on context. Hence, it is not a statement. Options A and D are false and option B is true.

The statement can be proved false if we can find a counterexample to the given statement. 2 is a prime number which is even. Hence, the statement is false.

A logical statement is a statement which has a definite truth value which is invariant. Here, options A, B and D have definite truth values. Option C may be true or false for different people.