Demonstratives adjectives are used to determine where an object, event or person is in relation to the speaker.
Question 1
(1) Esta
Esta translates into this in Spanish. We use it to describe a feminine and singular noun that is near the speaker and listener. Since the first sentence in English is This apple is sweet, then the sentence translates into:
Esta manzana es dulce
(2) Aquella
Aquella translates into that in Spanish. We use it to describe a feminine and singular noun that is far away from the speaker and the listener. Since the second sentence in English is That apple is sweeter, then the sentence translates into:
Aquella manzana es más dulce
(3) Aquella
In this case, we also use aquella because here the apple is also far away from the speaker and the listener. That is, But that apple over there is the sweetest translates into:
Pero aquella manzana es la más dulce
Question 2
(1) Esta
Esta translates into this in Spanish. We also need to use this demonstrative adjective here because the apple is near the speaker and the listener. So This apple is sweet translates into:
Esta manzana es dulce
(2) Esa
Esa translates into that in Spanish. We use it to describe a feminine and singular noun that is further from the speaker and not easily within reach. Since the second sentence in English is That apple is sweeter, then the sentence translates into:
Esa manzana es más dulce
(3) Aquella
Here we need to use aquella as well because here the apple is also far away from the speaker and the listener. That is, But that apple over there is the sweetest translates into:
Pero aquella manzana es la más dulce
Question 3
(1) Esta
Esta translates into this in Spanish. So this is the same option as in question 2.
Esta manzana es dulce
(2) Esa
Esa translates into that in Spanish. So this is the same option as in question 2
Esa manzana es más dulce
(3) Aquella
Aquella means that in Spanish and it is being used here as in question 2.
Pero aquella manzana es la más dulce