Aqua calida ad cubiculum portanda est.

Portanda est is a passive periphrastic: a gerundive (portanda) plus a form of esse (est).

It expresses necessity, obligation, or something that must be done.

So:

• portanda est = must be carried
• more literally = is to be carried

In this sentence, Aqua calida ad cubiculum portanda est means something like:

• The warm water must be carried to the bedroom
• or more literally, Warm water is to be carried to the bedroom

Because it agrees with aqua.

• aqua = feminine singular nominative
• portanda must match it in gender, number, and case

So:

• aqua → feminine singular nominative
• portanda → feminine singular nominative

This agreement is just like with ordinary adjectives. The gerundive behaves adjectivally.

Because Latin is using a passive-style construction, not an active one.

In English, we often think actively:

• Someone must carry the water

In Latin here, the sentence is framed passively:

• The water must be carried

That makes aqua the grammatical subject of the sentence, so it stands in the nominative.

So even though the water is the thing affected by the action, it is still nominative because it is the subject of portanda est.

They are not the same.

• portatur = it is carried / it is being carried
• portanda est = it must be carried / it has to be carried

So portatur states a fact or action. Portanda est adds the idea of necessity or duty.

Because calida modifies aqua and must agree with it.

• aqua = water
• calida = warm, hot

Since aqua is feminine singular nominative, calida is too.

So:

• aqua calida = warm water

Ad means to, toward, or in the direction of when there is motion toward a place.

Since the idea is carrying the water to the bedroom, Latin uses:

• ad
  • accusative

So:

• ad cubiculum = to the bedroom

If the meaning were in the bedroom rather than movement toward it, Latin would use a different expression, such as in cubiculo.

Because the preposition ad takes the accusative case.

So:

• ad + accusative = motion toward

Here:

• cubiculum is the accusative singular of cubiculum, a neuter noun meaning bedroom or chamber

Thus:

• ad cubiculum = to the bedroom

Yes, but Latin does not name that person here.

With the passive periphrastic, Latin can optionally add the dative of agent to show who has the obligation.

For example:

• mihi aqua calida ad cubiculum portanda est = I must carry the warm water to the bedroom
• literally, the warm water is to be carried by me / for me to carry

In your sentence, no agent is stated, so the meaning is more general:

• The warm water must be carried to the bedroom

Because Latin has no articles like English the or a/an.

So aqua can mean:

• water
• the water
• sometimes even some water

The exact sense depends on context.

That is very normal in Latin.

Latin word order is more flexible than English word order because the endings show the grammar.

This order is perfectly natural. It places:

• Aqua calida first: the thing being discussed
• ad cubiculum next: the destination
• portanda est at the end: the key verbal idea, must be carried

Other orders are possible, for example:

• Aqua ad cubiculum calida portanda est
• Portanda est aqua calida ad cubiculum

But the original order is clear and idiomatic.

Yes. Calidus, -a, -um can cover a range from warm to hot, depending on context.

So aqua calida could be:

• warm water
• hot water

The exact nuance depends on the situation.

Because the subject, aqua, is singular.

• aqua = singular
• therefore est = singular, not sunt

If the subject were plural, the verb and gerundive would also be plural. For example:

• Aquae calidae ad cubiculum portandae sunt = The warm waters must be carried to the bedroom or The containers of warm water must be carried to the bedroom, depending on context

It is a gerundive, not a gerund.

That matters because:

• a gerund is a verbal noun
• a gerundive is a verbal adjective

Here portanda agrees with aqua, so it is clearly adjectival. That makes it a gerundive.

In this construction, the gerundive expresses necessity:

• portanda est = must be carried

A very literal translation is:

• Warm water is to be carried to the bedroom

A more natural English translation is:

• The warm water must be carried to the bedroom

Both reflect the Latin well.