Serva calices e mensa removet et lucernam adhibet, ut mater epistulam clarius legere possit.

Yes, serva can be ambiguous when written without macrons:

• serva = the slave-girl / maid (nominative singular noun)
• servā = save! or keep! (imperative verb), if macrons are shown

In this sentence, it must be the noun, because the verb is removet = she removes. So serva is the person doing the action.

Calices is the direct object of removet, so it is in the accusative plural.

It comes from calix, calicis = cup or goblet.

Its accusative plural is calices.
By coincidence, the nominative plural is also calices, so you tell its role from the sentence:

• serva = subject
• removet = verb
• calices = thing being removed

So calices means the cups as the object.

Because Latin often uses a preposition for the idea from.

• e or ex = out of / from
• mensa is ablative singular after that preposition

So:

• e mensa = from the table

You could think of removet as removing the cups from the table, and Latin expresses that with e/ex + ablative.

Also, e and ex mean the same thing here. E is common before consonants, and ex is common before vowels, though usage is not completely rigid.

Because it follows the preposition e.

The preposition e/ex takes the ablative case, so:

• mensa = ablative singular of mensa
• e mensa = from the table

This is a very common pattern in Latin:
preposition + ablative for ideas like from, with, in, depending on the preposition.

Because lucernam is the direct object of adhibet.

• lucerna = lamp
• lucernam = accusative singular

So the maid adhibet lucernam = applies / brings / uses a lamp.

Even if the exact English wording varies, grammatically lucernam is the thing being acted upon, so it is accusative.

Literally, adhibet comes from adhibere, which can mean things like:

• bring to
• apply
• employ
• use

With lucernam, the idea is something like:

• she brings in a lamp
• she uses a lamp
• she puts a lamp to use

In context, the point is that the lamp is being used so the mother can read more clearly.

It is a purpose clause.

The conjunction ut can introduce different kinds of clauses, but here it means so that or in order that.

So the structure is:

• main action: Serva ... removet et lucernam adhibet
• purpose: ut mater epistulam clarius legere possit

In other words, the maid does these things so that the mother can read the letter more clearly.

Because it is inside a purpose clause introduced by ut.

In Latin, purpose clauses normally use:

• ut
  • subjunctive

So:

• possit = present subjunctive of possum
• not potest, which would be indicative

There is also a sequence-of-tenses reason:

• main verbs: removet and adhibet are present
• therefore Latin normally uses the present subjunctive in the purpose clause

So ut ... possit is exactly what you would expect.

Because it depends on possit.

Latin uses possum + infinitive to mean be able to do something:

• potest legere = he/she is able to read
• possit legere = he/she may be able to read or, in this context, can read

So:

• mater ... legere possit = the mother may be able to read

The infinitive legere gives the action that the mother is able to do.

Because clarius is the comparative adverb.

• clare = clearly
• clarius = more clearly

It modifies the verb legere, not a noun. So Latin needs an adverb, not an adjective.

That is why you get:

• epistulam clarius legere = to read the letter more clearly

A form like clarior would be an adjective, not the right form here.

Because mater is the subject of possit inside the ut clause.

In the subordinate clause:

• mater = subject
• epistulam = object
• legere possit = verb phrase

So the grammar is:

• mater does the reading
• epistulam is what is being read

That is why mater is nominative.

Because it is the direct object of legere.

• epistula = letter
• epistulam = accusative singular

So:

• mater epistulam legere possit = the mother can read the letter

The mother is the one reading; the letter is the thing being read.

Latin word order is much freer than English word order, because the case endings show the grammatical roles.

So Latin can say:

• Serva calices e mensa removet et lucernam adhibet, ut mater epistulam clarius legere possit

without needing a rigid English-style order.

A few things to notice:

• the main verb often comes near the end, but not always
• the purpose clause begins with ut
• clarius is placed near legere because it modifies the action of reading

So the order is natural Latin, even if it feels less straightforward than English at first.

Because the sentence describes two coordinated actions done by the same subject:

• Serva calices e mensa removet
• et lucernam adhibet

The word et joins the two verbs. Both have the same subject, serva, so Latin does not need to repeat it.

This is very common:

• one subject
• two verbs
• connected by et = and

So the maid removes the cups and uses/brings the lamp.