Tu letra se parece mucho a la de tu hermana.

Yes, letra can mean a letter of the alphabet, but it also commonly means handwriting in Spanish.

So in this sentence, tu letra means your handwriting, not your letter.

Examples:

• No entiendo tu letra. = I can’t read your handwriting.
• La letra A = the letter A

This is a very common use, so learners hear letra for handwriting a lot.

Because the verb here is parecerse a, which means to resemble / to be similar to.

So:

• parecer = to seem / to appear
• parecerse a = to look like / to resemble

Compare:

• Parece cansada. = She seems tired.
• Se parece a su madre. = She looks like her mother.

In your sentence, the structure is the second one:

• Tu letra se parece... = Your handwriting resembles...

The se is part of the verb parecerse.

Because parecerse is followed by a.

The pattern is:

parecerse a + person/thing

Examples:

• Me parezco a mi padre. = I look like my father.
• Esta casa se parece a la tuya. = This house looks like yours.
• Tu letra se parece a la de tu hermana. = Your handwriting looks like your sister’s.

So the a is required by the verb.

Here mucho works like an adverb and means a lot or very much.

It modifies se parece:

• se parece = resembles / looks like
• se parece mucho = resembles a lot / looks very similar

So:

• Tu letra se parece a la de tu hermana. = Your handwriting resembles your sister’s.
• Tu letra se parece mucho a la de tu hermana. = Your handwriting resembles your sister’s a lot / is very similar to your sister’s.

Because la stands for la letra.

Spanish often avoids repeating a noun if it is already clear. So:

• Tu letra se parece mucho a la letra de tu hermana.
  This is correct, but repetitive.

More natural:

• Tu letra se parece mucho a la de tu hermana.

Here la de tu hermana means the one of your sister, in other words, your sister’s handwriting.

This kind of shortening is very common in Spanish:

• Mi casa es más grande que la de Ana. = My house is bigger than Ana’s.
• Tu coche es más nuevo que el de Luis. = Your car is newer than Luis’s.

No, that would sound wrong.

The sentence is comparing handwriting with handwriting, not handwriting with your sister as a person.

So you need:

• Tu letra se parece mucho a la de tu hermana.

That means:

• your handwriting resembles your sister’s handwriting

If you said a tu hermana, it would sound as if the handwriting somehow resembles the sister herself, which is not the intended meaning.

Because tu without an accent is a possessive adjective meaning your.

• tu hermana = your sister
• tu letra = your handwriting

With an accent, tú is the subject pronoun you:

• Tú escribes muy bien. = You write very well.

So:

• tu = your
• tú = you

In this sentence, both are possessives, so neither has an accent:

• Tu letra se parece mucho a la de tu hermana.

Yes, absolutely. That is a very natural alternative.

Compare:

• Tu letra se parece mucho a la de tu hermana.
• Tu letra es muy parecida a la de tu hermana.

Both mean almost the same thing:

• se parece mucho a = looks a lot like / resembles
• es muy parecida a = is very similar to

Both are common and correct.

It is still handwriting in general.

Even though letra is singular, it can refer to a person’s writing style as a whole.

So:

• Tiene buena letra. = He/She has good handwriting.
• Tu letra es difícil de leer. = Your handwriting is hard to read.

This is just how Spanish expresses the idea. English uses the uncountable noun handwriting, while Spanish often uses singular letra.

The most natural order is:

Tu letra se parece mucho a la de tu hermana.

That is the standard placement.

You might sometimes hear other emphatic word orders in special contexts, but for normal speech and writing, keep mucho after se parece:

• se parece mucho a...

So as a learner, this is the safest pattern to use.

You would change the possessive words.

Examples:

• Mi letra se parece mucho a la de mi hermana. = My handwriting looks a lot like my sister’s.
• Su letra se parece mucho a la de su hermana. = His/Her/Your(formal) handwriting looks a lot like his/her/your sister’s.
• Vuestra letra se parece mucho a la de vuestra hermana. = Your(plural, Spain) handwriting looks a lot like your sister’s.

In Spain, vuestra/vuestro is used for you all’s in informal plural speech, while su can mean his, her, your formal, or their, depending on context.