Learn Turkish: Kâğıda bir cevap yazıyorum. - I am writing an answer on the paper.

The dictionary word is kâğıt (paper). When we add the dative suffix -a (meaning "to" or "on"), the final hard consonant t softens to a d. This is called consonant mutation, and it happens because the consonant gets sandwiched between two vowels, making it smoother to pronounce.

The word cevap ends in p. Why doesn't it change to b here?

Consonant mutation (like p turning into b) usually only happens when you add a suffix that starts with a vowel. Since cevap (answer) doesn't have any suffix attached to it in this sentence, its final letter stays exactly the same.

Why use the suffix -a on kâğıda instead of the locative suffix -da (on)?

In English, we say we write "on the paper," so you might expect the locative suffix -da (in/on/at). However, Turkish treats writing as a directional action. You are directing your words to the paper, so it takes the dative suffix -a (to).

What does the little hat on the â in kâğıda mean?

That mark is called a circumflex. In this word, it softens the k so it sounds a bit like "ky" and slightly lengthens the a sound. You will mostly see this mark on older words that Turkish borrowed from Arabic or Persian.