La risposta scritta è più chiara.

La is the definite article meaning the.

It is feminine singular because risposta is a feminine singular noun:

• la risposta = the answer

In Italian, articles are used more regularly than in English, so la risposta is the normal way to say the answer.

Here scritta means written.

It comes from the verb scrivere (to write), but in this sentence it is being used as an adjective:

• risposta scritta = written answer

So it describes what kind of answer it is.

Because scritta must agree with risposta.

In Italian, adjectives usually agree with the noun they describe in gender and number:

• risposta = feminine singular
• so the adjective must also be feminine singular
• therefore: scritta

Compare:

• il messaggio scritto = the written message
• la risposta scritta = the written answer

For the same reason: adjective agreement.

Chiara comes from chiaro (clear), but it changes form to match risposta, which is feminine singular:

• masculine singular: chiaro
• feminine singular: chiara
• masculine plural: chiari
• feminine plural: chiare

So:

• la risposta è chiara
• la risposta scritta è più chiara

Più means more, so più chiara literally means more clear.

In natural English, this is often translated as clearer.

So:

• chiara = clear
• più chiara = clearer / more clear

Italian often uses più + adjective where English may use -er:

• più grande = bigger
• più semplice = simpler
• più chiara = clearer

Yes, it usually implies some kind of comparison, even if the second part is not stated.

So La risposta scritta è più chiara can mean:

• The written answer is clearer
• The written answer is clearer than the spoken one
• The written answer is clearer than before
• The written answer is clearer this way

Italian often leaves the comparison understood from context.

If you want to state it explicitly, you can add di:

• La risposta scritta è più chiara di quella orale.
• The written answer is clearer than the oral one.

È is the verb is from essere (to be).

It has an accent to distinguish it from e, which means and:

• è = is
• e = and

So:

• La risposta scritta è più chiara. = The written answer is clearer.
• pane e acqua = bread and water

This accent is very important in writing.

In Italian, adjectives often come after the noun, especially when they are descriptive.

So:

• risposta scritta = written answer
• risposta chiara = clear answer

That said, adjective placement in Italian can sometimes vary for style or emphasis, but in this sentence the normal order is:

• noun + adjective
• la risposta scritta

And then after the verb:

• è più chiara

So the structure is:

• La risposta scritta = subject
• è = verb
• più chiara = complement

In Italian, ch before i or e has a hard k sound.

So chiara is pronounced roughly:

• KYAH-ra

More accurately:

• kià-ra

Important point:

• ci = usually a soft ch sound, like in cena
• chi = hard k sound

So:

• chiara does not sound like English chaira
• it starts with a k sound

Here it functions as an adjective, even though it comes from a verb.

It is the past participle of scrivere, but in this sentence it describes the noun:

• la risposta scritta = the written answer

So grammatically, it behaves like an adjective because it agrees with risposta:

• feminine singular → scritta

This is very common in Italian:

• una lettera scritta bene = a well-written letter
• un libro pubblicato recentemente = a recently published book

Yes, but that means something slightly different.

• La risposta scritta è più chiara = The written answer is clearer
  This treats written answer as one noun phrase.

• La risposta è più chiara se è scritta = The answer is clearer if it is written
  This adds a condition: it is clearer when/if it is written.

So your original sentence is shorter and more compact, while the second version spells the idea out more explicitly.