Serva hospiti panem et aquam in mensa proponit.

Because serva is in the nominative singular, which is the case normally used for the subject.

Here, serva means the female servant / maidservant. The ending -a is the regular nominative singular ending for many first-declension feminine nouns.

So serva ... proponit means the servant ... sets out / places.

Hospiti is dative singular.

It is used because the guest is the indirect object: the bread and water are being set out for the guest.

So the roles are:

• serva = subject
• panem et aquam = direct objects
• hospiti = indirect object

If it were hospitem, that would be accusative singular, which would suggest the guest was a direct object instead.

The dictionary form is hospes, hospitis (guest / host), a third-declension noun.

They are both in the accusative singular, because they are the direct objects of proponit.

The servant is setting out:

• panem = bread
• aquam = water

So:

• panis → panem in the accusative singular
• aqua → aquam in the accusative singular

Latin marks direct objects with case endings, instead of relying mostly on word order the way English does.

Because in can take two different cases depending on the meaning:

• in + ablative = in / on a place, with no motion
• in + accusative = into / onto a place, with motion toward it

Here, in mensa means on the table or upon the table as a location, so Latin uses the ablative:

• mensa = ablative singular

If the idea were onto the table as motion toward it, Latin would use in mensam.

Proponit is from proponere.

Its basic idea is to place before, and in this kind of context it can mean:

• sets out
• places before
• serves
• puts on the table

It is:

• 3rd person singular
• present tense
• active
• indicative

So proponit means he/she sets out or he/she places before. Since the subject is serva, here it means she sets out.

In Latin, case endings usually matter more than word order.

English depends heavily on position:

• The servant serves the guest bread is different from
• The guest serves the servant bread

Latin, however, shows the job of each word by its ending:

• serva = nominative subject
• hospiti = dative indirect object
• panem et aquam = accusative direct objects
• in mensa = ablative phrase

So even if the sentence were rearranged, the meaning would stay mostly the same, for example:

• Panem et aquam serva hospiti in mensa proponit.
• Hospiti serva in mensa panem et aquam proponit.

The emphasis might shift, but the grammar still tells you who is doing what.

Because classical Latin has no articles.

So a noun like serva can mean:

• a servant
• the servant

Likewise:

• hospiti = to a guest or to the guest
• panem = bread / a loaf / the bread, depending on context

You determine whether English should use a or the from the context, not from a separate Latin word.

On its own, serva could indeed be an imperative form of servare, meaning save! or preserve!

But in this sentence, it is clearly a noun, not a verb.

Why?

Because the sentence already has its main finite verb: proponit.
Also, the whole structure makes sense with serva as the subject:

• The servant sets out bread and water for the guest on the table

So although serva can be ambiguous in isolation, the sentence structure removes the ambiguity.

It is singular: to/for the guest.

If it were plural, you would expect hospitibus:

• hospiti = to/for the guest
• hospitibus = to/for the guests

This is a common third-declension dative plural ending: -ibus.

Latin often uses singular nouns for substances or mass nouns just as English does.

So:

• panem = bread
• aquam = water

Even though English sometimes says some bread or some water, Latin often just uses the singular noun without a word meaning some.

Depending on context, panem could refer to bread generally or to a loaf / portion of bread.

They are:

• serva, servae = female servant, maidservant
• hospes, hospitis = guest, host
• panis, panis = bread, loaf
• aqua, aquae = water
• mensa, mensae = table

Knowing the dictionary form helps you identify the declension and understand why the forms in the sentence look the way they do:

• serva = nominative singular
• hospiti = dative singular
• panem = accusative singular
• aquam = accusative singular
• mensa = ablative singular after in

Literally, in often means in, but with places it can also mean on, depending on context.

With mensa (table), the natural English translation is usually on the table, not in the table.

So in mensa is one of those cases where you should translate for natural English sense, not word-for-word in a mechanical way.

Yes. Latin often leaves out the subject pronoun or even the subject noun when it is already clear.

Because proponit already means he/she/it sets out, a sentence like this could simply say:

Hospiti panem et aquam in mensa proponit.

That would mean She sets out bread and water for the guest on the table, if the context already made clear who she was.

In this sentence, serva is included for clarity or emphasis.