Feles ex cellario exit et murem quaerit.

The preposition ex means out of or from inside. It needs a noun in the ablative case, so cellario is ablative singular.

So:

• ex = out of / from
• cellario = from the cellar/store-room

Together, ex cellario means out of the cellar.

Because the preposition ex always takes the ablative. This is a standard Latin rule.

The noun is cellarium. Its ablative singular form is cellario. So:

• cellarium = cellar, pantry, store-room
• ex cellario = out of the cellar / from the pantry

Because murem is the accusative singular form, and the direct object of a verb is usually put in the accusative in Latin.

Here the cat is looking for the mouse, so the mouse is the direct object of quaerit.

• nominative: mus = a mouse
• accusative: murem = a mouse, as the object

Exit is the third-person singular present active indicative of exire, meaning to go out or to come out.

So exit means:

• he/she/it goes out
• he/she/it comes out
• in this sentence: the cat comes out/goes out

Quaerit is the third-person singular present active indicative of quaerere, meaning to seek, look for, or search for.

So murem quaerit means she is looking for a mouse or the cat looks for a mouse.

Classical Latin does not have articles like English the and a/an. Whether you translate a noun as cat, the cat, or a cat depends on context.

So:

• feles could be the cat or a cat
• murem could be the mouse or a mouse

English usually has to choose, but Latin often leaves that unstated.

Yes. Latin word order is much more flexible than English word order because the endings show what each word is doing.

This sentence could be rearranged in several ways and still mean basically the same thing, for example:

• Ex cellario feles exit et murem quaerit
• Feles murem quaerit et ex cellario exit

The exact order can change the emphasis or style, but the case endings and verb forms keep the grammar clear.

Usually, yes. Et is the common Latin word for and. Here it simply joins two actions done by the same subject:

• exit = comes out
• quaerit = looks for

So the cat comes out and looks for the mouse.

Both verbs, exit and quaerit, are third-person singular, and there is only one expressed subject, feles. In Latin, when one subject is followed by multiple matching verbs joined by et, that subject is understood with both verbs unless something else is stated.

So the sentence means:

• The cat comes out of the cellar and looks for a mouse.

The main dictionary forms are:

• feles, felis — cat
• ex — out of, from
• cellarium, cellarii — cellar, pantry, store-room
• exeo, exire — go out, come out
• et — and
• mus, muris — mouse
• quaero, quaerere — seek, look for

This is useful because Latin sentences usually contain inflected forms rather than the exact dictionary forms.

Yes. The Latin present tense often covers both simple present and progressive present in English.

So quaerit can be translated as:

• seeks
• is seeking
• looks for
• is looking for

The best English choice depends on the context and the style of translation.