Ante cenam manus lavandae sunt.

Because ante is a preposition that takes the accusative. So when Latin says ante cenam, cena appears as cenam.

Here ante cenam means before dinner. This is just normal prepositional usage:

• ante = before
• cenam = accusative singular of cena

Here it is plural: hands.

A beginner often gets confused because manus belongs to the fourth declension, and without macrons several forms look the same in writing. The key clue is agreement:

• lavandae is feminine plural
• sunt is plural

So manus must also be understood as plural in this sentence.

Many Latin nouns ending in -us are masculine, especially in the second declension, but manus is a fourth-declension noun and is usually feminine.

So:

• manus = hand
• gender: feminine
• declension: fourth declension

That is why the gerundive is lavandae, not lavandi or lavanda.

Lavandae is the gerundive of lavare, meaning something like to be washed or needing to be washed.

In this sentence it agrees with manus:

• feminine
• plural
• nominative

So manus lavandae means hands needing to be washed or more naturally hands that must be washed.

Because lavandae sunt expresses necessity or obligation, not just a plain passive action.

Compare:

• lavantur = they are being washed / they are washed
• lavandae sunt = they must be washed / they need to be washed / they are to be washed

This construction is called the passive periphrastic:

• gerundive + a form of sum

It is one of the standard Latin ways to express must.

Because it goes with manus, which is plural here.

The basic structure is:

• manus = subject
• lavandae = adjective agreeing with manus
• sunt = plural form of to be

So Latin is literally saying something like the hands are needing-to-be-washed, which is the idiomatic way to say the hands must be washed.

Latin often leaves the agent unstated in this construction when it is general or obvious.

So Ante cenam manus lavandae sunt can mean:

• Hands must be washed before dinner
• One must wash one’s hands before dinner

If Latin wanted to name the person responsible, it could use the dative of agent:

• mihi manus lavandae sunt = I must wash my hands
  literally, the hands are to-be-washed for me

Since there is no agent here, the statement is general.

Yes. That is a very natural English rendering.

Latin often uses a passive-looking structure where English prefers an active one. So:

• literal Latin structure: Before dinner, the hands must be washed
• natural English: Before dinner, one must wash one’s hands

Both reflect the same idea.

The finite verb sunt is present tense, so the sentence expresses a present rule, necessity, or general obligation.

It does not simply mean future time. The sense is:

• must be washed
• should be washed
• need to be washed

So it is best understood as a present statement of obligation.

Yes. Latin word order is flexible because the endings show the grammatical relationships.

This sentence puts Ante cenam first to set the time immediately: before dinner. Then it gives the subject and obligation:

• manus lavandae sunt

Other orders are possible, such as:

• Manus ante cenam lavandae sunt
• Lavandae sunt ante cenam manus

But the given order is natural and clear:

1. time phrase first
2. then the main statement

Yes, grammatically it behaves like an adjective, because the gerundive agrees with a noun in gender, number, and case.

Here it agrees with manus:

• manus = feminine plural nominative
• lavandae = feminine plural nominative

So although it comes from a verb, it functions adjectivally in the sentence. That is why it matches manus in form.