Serva tunicam laceram sarcire conatur, sed filum nimis breve est.

Because both words are feminine singular accusative.

• tunicam is the direct object: it is the thing being mended.
• laceram is an adjective meaning torn or ragged, and it must agree with tunicam in gender, number, and case.

So tunicam laceram means the torn tunic.

Sarcire is the present active infinitive, meaning to mend or to repair. In Latin, the infinitive is a single word; there is no separate word corresponding to English to.

So:

• sarcire = to mend
• conatur sarcire = tries to mend

Because conor, conari, conatus sum is a deponent verb. Deponent verbs use passive-looking forms but have active meanings.

So conatur is:

• 3rd person singular
• present indicative
• active in meaning

It means she tries or she is trying, not she is tried.

It is the object of sarcire.

The structure is:

• serva = subject
• sarcire = infinitive
• tunicam laceram = object of that infinitive
• conatur = main verb

So the sentence works like this:

The slave-girl tries [to mend the torn tunic].

In sed filum nimis breve est, the verb is est, so the clause needs a subject. Filum is that subject: the thread.

A point that often confuses learners is that neuter nouns have the same form in nominative and accusative singular. So filum could theoretically be either by form alone. But here, with est, it clearly functions as nominative: the thread is too short.

Because filum is neuter, and the adjective must agree with it.

The adjective is brevis, breve:

• masculine/feminine nominative singular: brevis
• neuter nominative singular: breve

So:

• filum breve = a short thread

Nimis is an adverb meaning too, overly, or excessively. It modifies breve.

So:

• breve = short
• nimis breve = too short

Latin does not have articles like English the and a/an. A noun by itself can mean either a ... or the ..., depending on context.

So:

• serva can mean a slave-girl or the slave-girl
• filum can mean a thread or the thread

The translation decides which sounds most natural in English.

Not really. Latin word order is much freer than English word order because the endings show what each word is doing.

A few normal features here are:

• the main verb conatur comes at the end of its clause
• the infinitive phrase tunicam laceram sarcire comes before conatur
• sed introduces the second clause

So the Latin order is different from English, but it is very natural Latin.