1. cuál
¿Cuál aerolínea prefieren Uds?
Since aerolínea, that translates into airline, is a singular noun, we need to use the word cuál that matches this type of nouns. If a question implies a choice between two or more alternatives and conveys the idea of selection, we must use the following formula:
¿Cuál + singular noun?
2. cuáles
¿Cuáles canciones españolas conoces?
Since canciones, that translates into songs, is a plural noun, we need to use the word cuáles that matches this type of nouns. So in this question I want to know which Spanish songs do you know? In this way, you might answer something like this:
Yo conozco las baladas y las canciones de cumpleaños
3. cuál
¿Cuál tipo de libro le gusta?
Since tipo, that translates into kind, is a singular noun, we need to use the word cuál that matches this type of nouns. So in this question le represents the indirect object pronoun either for the pronouns él and ella or usted (formal you). Perhaps I want to know either what type of books you or he (or she) would rather.
4. cuál
¿Cuál tren toma él?
Since tren, that translates into train, is a singular noun, we need to use the word cuál that matches this type of nouns. Here we want to know what train he takes. So toma is the conjugation of the verb tomar (to take) for the third person singular in the simple present. In this sentence, this person is él that matches he in English.
5. cuáles
¿Cuáles diarios compran ellos?
Since diarios, that translates into newspapers, is a plural noun, we need to use the word cuáles that matches this type of nouns. Here we want to know what newspapers they buy. So compran is the conjugation of the verb comprar (to buy) for the third person plural in the simple present.
6. cuáles
Me gustan estos diarios. ¿Cuáles te gustan?
In the question ¿Cuáles te gustan? I must assume that the speaker asks me for the type of newspaper (diarios) I like to read. Since we are in this context and diarios is a plural noun, then we must choose cuáles. Moreover, te is the indirect object pronoun for the second person singular and gustan matches this person as well.
7. cuáles
Ella escucha una canción puertorriqueña y una canción mexicana. ¿Cuál prefiere ella?
This question implies a choice between two alternatives and conveys the idea of selection. Since the questions asks for an only selection (singular form), we need to choose cuál. On the other hand, prefiere is the conjugation of the verb preferir for the third person singular in the simple present. Here this person is ella that is feminine and means she.
8. esta
Me gusta esta corbata
This question stands for demonstrative adjectives. So these adjectives demonstrate a quality about the noun they modify. Here that quality is the location in respect to the speaker or the listener. So esta is used to point out something near to the speaker in space or time.
9. esa
Me gusta esa corbata
This question also stands for demonstrative adjectives. Since you like the tie farthest from you, then the demonstrative adjectives you must use is esa. This indicates something more distant, that is, nouns that are further from the speaker but they can be close to the listener.
Note. You can also use aquella if the tie is far away from both the speaker and the listener.