Sed amica mea audet etiam sententias difficiliores statim scribere.

Amica mea is the subject of the sentence, so both words are in the nominative singular feminine:

• amica = nominative singular of amica
• mea = nominative singular feminine of meus, mea, meum

They agree because mea is a possessive adjective modifying amica.

Latin word order is more flexible than English word order. Both amica mea and mea amica are possible.

With possessives, Latin often places the possessive adjective after the noun, especially in simple, natural phrasing. So amica mea is a very normal way to say my friend.

The difference is usually not a big one in a sentence like this; it is mostly a matter of style and emphasis.

Audet means she dares, and scribere means to write.
Latin commonly uses a finite verb plus an infinitive in this pattern:

• audet scribere = she dares to write

This is called a complementary infinitive: the infinitive completes the meaning of the main verb.

So:

• audet = 3rd person singular present active of audeo, audere
• scribere = present active infinitive of scribo, scribere

Because Latin infinitives already include the idea of to in a single word.

So:

• scribere = to write

Latin does not need an extra separate word like English to here.

Because sententias is the direct object of scribere: it is the thing being written.

• scribere quid? = to write what?
• Answer: sententias

Sententia is a first-declension noun, so its accusative plural ends in -as:

• nominative singular: sententia
• accusative plural: sententias

Difficiliores is a comparative adjective from difficilis (difficult). It agrees with sententias in:

• gender: feminine
• number: plural
• case: accusative

So:

• sententias = accusative plural feminine
• difficiliores = accusative plural feminine (also masculine in form)

Together they mean more difficult sentences.

Comparative adjectives in Latin often use forms in -ior / -ius, and they decline like third-declension adjectives.

Because quam is only needed when Latin explicitly states the second side of the comparison.

For example:

• sententias difficiliores quam illas = sentences more difficult than those

But if the sentence simply says more difficult sentences without naming what they are being compared with, Latin can just use the comparative adjective by itself:

• sententias difficiliores

Etiam means also or even, depending on context and emphasis.

Here it adds the idea that the friend dares to do this as well, or perhaps even this surprisingly difficult thing. It is emphasizing the phrase that follows, especially sententias difficiliores.

Latin adverbs like etiam are fairly movable, and their position can slightly affect emphasis more than basic meaning.

Statim is an adverb meaning immediately, at once, or right away. It modifies the action scribere:

• statim scribere = to write immediately

It tells us how quickly she writes them.

That placement is normal Latin style. Adverbs often appear near the word they modify, but Latin does not require the fixed word order that English does.

So statim scribere is a natural way to say to write immediately.
Latin could move statim elsewhere for a different rhythm or emphasis, while keeping essentially the same basic meaning.

Yes. Latin word order is much more flexible than English word order because grammatical endings show the function of the words.

For example, the sentence could be rearranged in several ways without changing the core meaning, such as:

• Sed mea amica etiam sententias difficiliores statim scribere audet.
• Sed etiam amica mea sententias difficiliores statim scribere audet.

The exact order mainly changes emphasis, focus, or style, not the basic grammatical relationships.