Amicitia mihi magni pretii est.

Amicitia is nominative singular. It is the subject of est, so it names the thing being described: friendship.

It is the first-declension noun amicitia, amicitiae.

Mihi is the dative singular of ego (I).

Here it means to me or for me. Latin often uses the dative with esse to show the person from whose point of view something is true. So:

• Amicitia mihi ... est = Friendship is ... to me / for me

This is often called a dative of reference.

Magni pretii means of great value or more literally of great price.

The two words go together:

• pretii = of price / of value
• magni = great, in the form that agrees with pretii

So the whole phrase describes amicitia as something very valuable.

Both are genitive singular.

• pretii is the genitive singular of pretium
• magni is the genitive singular of magnus, agreeing with pretii

This kind of phrase is a standard Latin way to express value: of great value, of small value, and so on.

Because magni agrees with pretii, not with amicitia.

A learner may first think: amicitia is feminine, so why not magna? But the adjective is not modifying amicitia directly. It is modifying pretii inside the genitive phrase magni pretii.

So:

• not friendship great
• but friendship of great value

That is why the adjective takes the genitive singular form magni.

Est is the usual verb is.

It links the subject amicitia with the description magni pretii. So the structure is basically:

• Amicitia = subject
• mihi = to me / for me
• magni pretii = of great value
• est = is

So the sentence means literally something like:

Friendship is of great value to me.

A very literal translation would be:

Friendship to me of great value is.

That is not natural English, of course, but it helps show how the Latin sentence is built.

Because Latin word order is much freer than English word order.

English usually depends heavily on position to show grammatical relationships. Latin does that mostly through endings, so the order can be arranged for emphasis or style.

In this sentence:

• Amicitia comes first as the topic
• mihi appears early to show the personal point of view
• magni pretii is kept together as the key description
• est comes last, which is very common in Latin

Yes. Because the endings show the grammar, Latin allows several possible orders, for example:

• Mihi amicitia magni pretii est
• Amicitia magni pretii mihi est
• Magni pretii mihi amicitia est

These would all mean basically the same thing, though the emphasis may shift a little. The given order is perfectly natural.

You can build similar phrases. Latin commonly uses expressions like this to talk about value.

Examples of the same pattern include:

• parvi pretii = of small value
• maximi pretii = of the greatest value
• magno pretio is different and usually means for a high price in a different construction

So magni pretii est is not just an isolated phrase; it belongs to a larger pattern.

Yes. A simpler Latin sentence might be:

• Amicitia mihi cara est = Friendship is dear to me

That is a little more direct and emotionally colored.
Amicitia mihi magni pretii est sounds more like Friendship is of great value to me, which stresses worth rather than just affection.