This is a very $\color{blue}{\text{Poor Question. }}$
In GATE, TIFR like exams, such question can never be asked. So, $\color{red}{\text{DO NOT }}$ waste your time on such questions.
Whether we allow "Today is Sunday" as a proposition or not, depends on the context in which we're going to evaluate it (how are we going to account for changing time?), not on the simple definition of "a proposition".
If we can make it into something that's either true or false then we can use it as a proposition.
If we're stuck saying, "well, it depends when you say it" then perhaps we can't (or perhaps we can, but it remains a variable in whatever logical operations we do to it).
So, $\color{blue}{\text{Some authors }}$ would consider it as a proposition (by fixing certain time, date, place etc), $\color{blue}{\text{Other authors }}$ would not consider it as a proposition.
I suggest $\color{red}{\text{NOT to waste too much time }}$ on “which sentence is proposition?” type of question.
A Good exam will not ask such questions. If you find such questions in some test series, leave such test series.
In the (good)question, propositions will be $\color{blue}{\text{given }}$, not asked.
https://math.stackexchange.com/questions/3366696/how-to-determine-a-sentence-is-proposition-or-not
https://math.stackexchange.com/questions/1915208/identifying-propositions
If you are preparing for $\color{red}{\text{NET exam, }}$ then from the Options we can decide whether the question maker considers Statement(iii) as a proposition or not.
Clearly, Statement(ii) is a Question, so, Not a proposition.
Statement(iv) is a command/advice, so, Not a proposition.
Automatically, Option A is correct answer.
