Avia dicit amicitiam bonam servandam esse.

Because this sentence uses indirect statement, a very common Latin construction after verbs like dicit (says).

In an indirect statement, Latin normally uses:

• an accusative subject
• plus an infinitive

So in Avia dicit amicitiam bonam servandam esse, the whole part amicitiam bonam servandam esse is what the grandmother says.

Here, amicitiam is the accusative subject of that infinitive clause.

A useful comparison:

• Amicitia bona servanda est = A good friendship must be preserved / Friendship should be preserved
• Avia dicit amicitiam bonam servandam esse = Grandmother says that a good friendship must be preserved

When that statement gets reported after dicit, amicitia changes to amicitiam.

Servandam esse is made of:

• servandam = the gerundive of servare
• esse = to be

Together they form the passive periphrastic, which expresses necessity, obligation, or something that ought to be done.

So:

• servandam esse = to have to be preserved
• or more naturally, must be preserved / should be preserved

This is not just a plain infinitive like servare (to preserve). It specifically adds the idea of duty or necessity.

A gerundive is a verbal adjective. It often has the sense to be ...-ed or needing to be ...-ed.

Here it comes from servare (to preserve, keep, maintain):

• masculine nominative singular: servandus
• feminine nominative singular: servanda
• feminine accusative singular: servandam

It is feminine singular accusative because it agrees with amicitiam, which is also:

• feminine
• singular
• accusative

So:

• amicitiam bonam servandam all agree with one another.

Because bonam is an adjective modifying amicitiam.

Since amicitiam is:

• feminine
• singular
• accusative

the adjective must match it:

• amicitiam bonam = a good friendship

This is normal Latin adjective agreement.

Because the sentence is inside an indirect statement, and the predicate of that indirect statement is an infinitive.

The basic direct form would be:

• Amicitia bona servanda est

When reported after dicit, Latin changes est to esse:

• amicitiam bonam servandam esse

So esse is there because the whole reported statement must be expressed with an infinitive.

Not if you want the same meaning.

• servare means simply to preserve
• servandam esse means must be preserved or needs to be preserved

So the two are grammatically and semantically different.

For example:

• Avia dicit amicitiam bonam servare would not mean the same thing, and as it stands it would also be incomplete or awkward.
• Avia dicit amicitiam bonam servandam esse clearly expresses obligation.

The sentence does not explicitly say.

Latin often leaves that unstated when the idea is general, like English one should preserve friendship or friendship should be preserved.

If Latin wanted to name the person who has the obligation, it often uses the dative of agent with the passive periphrastic.

For example:

• Avia dicit nobis amicitiam bonam servandam esse
• Grandmother says that we must preserve a good friendship

Here nobis would mean for us / by us / we are the ones who must.

So in your sentence, the duty is general or left understood.

Not directly.

The direct object of dicit is really the entire indirect statement:

• amicitiam bonam servandam esse

Within that clause, amicitiam is the accusative subject of the infinitive construction.

So it may look like amicitiam is the object of dicit, but grammatically it belongs to the indirect statement, not as a simple standalone object.

The direct version would be:

• Amicitia bona servanda est.

That means:

• A good friendship must be preserved
• or Good friendship should be maintained

Then, when reported after Avia dicit, it becomes:

• Avia dicit amicitiam bonam servandam esse.

This is a very useful transformation to recognize:

• direct: servanda est
• indirect: servandam esse

Yes. It is passive in form and sense.

Compare:

• servat = he/she preserves
• servatur = it is preserved
• servanda est = it must be preserved

The passive periphrastic combines passive meaning with obligation.

So amicitiam bonam servandam esse means not to preserve a good friendship, but for a good friendship to have to be preserved.

Yes, Latin word order is flexible.

Your sentence is:

• Avia dicit amicitiam bonam servandam esse.

But Latin could also say things like:

• Avia bonam amicitiam servandam esse dicit.
• Amicitiam bonam avia servandam esse dicit.

The meaning stays basically the same, though emphasis may shift.

In your sentence, the order is quite natural:

• Avia = subject first
• dicit = main verb
• then the reported statement
• with esse at the end, which is very common in infinitive clauses

It comes from servare, which can mean things like:

• save
• preserve
• keep
• maintain

In the context of amicitia (friendship), the most natural English sense is:

• preserve
• maintain
• keep up

So the idea is not usually rescue a friendship from danger in a dramatic sense, but more generally maintain or preserve friendship.

A good step-by-step approach is:

1. Avia dicit = Grandmother says
2. After dicit, expect possible indirect statement
3. Spot esse = infinitive
4. Spot amicitiam = accusative subject of the infinitive clause
5. Spot servandam agreeing with amicitiam
6. Understand gerundive + esse = obligation

So you can mentally parse it as:

• Grandmother says
• that friendship
• good
• must be preserved

Then smooth it into natural English.