Servus aquam calidam ad cubiculum portat.

Because servus is in the nominative singular, which is the usual case for the subject of a sentence. In a dictionary, the basic form you see for a noun is typically the nominative singular (so servus = slave/servant).

Aquam is the direct object—the thing being carried—so Latin puts it in the accusative singular. For many 1st-declension nouns like aqua, the accusative singular ends in -am (so aqua → aquam).

Calidam is an adjective meaning warm/hot, describing aquam. Latin adjectives generally agree with the noun they modify in case, number, and gender.

• aquam = accusative singular feminine
• calidam = accusative singular feminine
  So they “match” because they belong together: aquam calidam = warm water.

Both are possible. Latin word order is flexible:

• aquam calidam is common and straightforward.
• calidam aquam is also fine and can give the adjective a bit more emphasis.
  Agreement (matching endings) is what keeps the meaning clear.

Ad is a preposition meaning to/toward, and it typically takes the accusative. So cubiculum is accusative after ad:

• ad cubiculum = to the bedroom

Because cubiculum is neuter (2nd declension). In the 2nd declension, neuter nominative singular and neuter accusative singular are identical in form:

• nominative: cubiculum
• accusative: cubiculum

No, because the endings tell you the roles:

• servus (nominative) = subject = the one doing the carrying
• aquam calidam (accusative) = direct object = what is carried
• ad cubiculum (ad + accusative) = destination
  So even if you rearranged the words, the cases would still point to the same basic meaning.

Portat is 3rd person singular present indicative active: (he/she/it) carries.
The dictionary form is usually porto, portare (to carry). The pattern is:

• porto = I carry
• portat = he/she/it carries

Classical Latin has no definite or indefinite articles. So servus can mean a slave or the slave, depending on context. Same with cubiculum: a/the bedroom.

In classical pronunciation, final -m is often very lightly pronounced and can sound like nasalization of the preceding vowel (so aquam may sound closer to aquã). In writing, you must keep the -m.

Servus literally means slave in Roman contexts, but it can be translated servant in smoother English depending on the setting. The Latin word itself strongly leans toward slave, with context guiding how you render it.

Add non before the verb (or before what you want to negate):

• Servus aquam calidam ad cubiculum non portat. = The slave does not carry warm water to the bedroom.