accent on Está
 

When should you remove the accent mark on a in "Está".

I understand that in interrogative statements it should be "Está".

What are the scenarios in which I need to remove the accent mark?

esta means this. Está means is from the verb estar. I am = estoy, you are (informal)=estásyou are (formal), he is, she is, it is= está, etc.

From the verb estar (always use the accent on the last a):

(Usted/el/ella) está.
You/he/she/it is here.

(Tú) estás.
You are here.

The demonstrative pronoun when modifying a noun never takes an accent:

Esta carta me partió el alma.
This letter broke my heart.

Estas personas vienen por primera vez.
These people are here for the first time.

The demonstrative pronoun when used as a noun takes an accent on the first e.

Ésta es la carta que me partió el alma.
This one is the letter that broke my heart.

For that motive, I love this website, my partners always has an answer for you.

las manzañas están verdes.

Is the accent on a correct?

The accent on the 'a' of están is correct.

The sentence you wrote has a misspelling, however, and should read:

Las manzanas están verdes.
This sentence means that the apples are green at the present time (they are unripe, not ready to eat).

Las manzanas son verdes.
This sentence describes apples that are characteristically green, like Granny Smith apples, when ripe (ready to eat).