Which of the following sentences is grammatically correct?

The correct answer is Option (4) → After the match, the coach discussed the new batting order with Ishaan and me.

Pronoun after a preposition:

“With” is a preposition. A pronoun that comes after a preposition takes the object form (me, him, her, us, them). Here both “Ishaan” and “me” come after “with”, so “me” is right. The sentence has no other error.

Why the Other Options are Incorrect?

Option 1: Do you know who’s water bottle was left in the staff room? — Incorrect. The given sentence says “who’s water bottle”. This is wrong: “who’s” is short for “who is” or “who has”. To show belonging before a noun, use “whose”.
Corrected: Do you know whose water bottle was left in the staff room?

Option 2: The players blamed theirselves for dropping three easy catches. — Incorrect. The given sentence says “theirselves”. This is wrong: the reflexive form for “they” is built on “them”, not on “their”.
Corrected: The players blamed themselves for dropping three easy catches.

Option 3: The new app who shows the live location of our school bus has made mornings easier. — Incorrect. The given sentence says “The new app who”. This is wrong: “who” is used only for people. An app is a thing, so use “which”.
Corrected: The new app which shows the live location of our school bus has made mornings easier.