Una puella in commentario suo scribit senatum decreta facere, oratores autem in contione populum movere conari.

Because this sentence uses indirect statement after scribit.

After verbs like say, think, know, hear, write, Latin often does accusative + infinitive instead of using that + a finite verb. So:

• senatum decreta facere = that the senate makes decrees
• oratores ... populum movere conari = that the orators are trying to move the people

In each indirect statement:

• the subject goes into the accusative
• the verb goes into the infinitive

So senatum is accusative because it is the subject of facere inside indirect statement.

For the same reason. Oratores is the subject of conari inside the second indirect statement.

So the structure is:

• scribit = she writes
• senatum decreta facere = that the senate makes decrees
• oratores autem in contione populum movere conari = but that the orators in the assembly are trying to move the people

Even though oratores looks like it could be nominative plural, here it is actually accusative plural as well. For third-declension nouns like orator, nominative plural and accusative plural are different:

• nominative plural: oratores
• accusative plural: oratores

So the form happens to be the same.

Because they belong to indirect statement after scribit.

English says:

• she writes that the senate makes decrees
• she writes that the orators try to move the people

Latin usually says:

• she writes the senate to make decrees
• she writes the orators to try to move the people

That sounds strange in English, but that is the normal Latin pattern:

• accusative subject
• infinitive verb

So facere and conari are exactly what you would expect in this construction.

Literally it means to make decrees.

• decreta = decrees
• facere = to make, do

This is a common Latin way to express the idea of issuing or passing decrees. Depending on context, English might translate it as:

• make decrees
• pass decrees
• issue decrees

Because conor, conari, conatus sum is a deponent verb.

A deponent verb:

• has mostly passive-looking forms
• but an active meaning

So:

• conari looks like a passive infinitive
• but it means to try, not to be tried

That is completely normal for deponent verbs in Latin.

It means to try to move the people.

Break it down like this:

• populum = the people
• movere = to move
• conari = to try

Here conari takes another infinitive, movere. So the sense is:

• oratores ... conari = the orators are trying
• populum movere = to move the people

Together: the orators are trying to move the people.

Autem is a mild contrast word, often meaning:

• but
• however
• on the other hand

Here it contrasts the two parts of the indirect statement:

• the senate makes decrees
• the orators, however, try to move the people

A useful thing to remember is that autem often comes second in its clause, not first. So Latin likes:

• oratores autem rather than
• autem oratores

It means in the assembly or at a public meeting.

• contio is a public gathering, meeting, or assembly, especially one where speaking takes place.
• in
  • ablative gives location: in the assembly

So oratores autem in contione means the orators, however, in the assembly...

Both are possible.

Latin word order is flexible, and adjectives or possessives can appear before or after the noun. So both of these can mean in her notebook:

• in commentario suo
• in suo commentario

The version in your sentence is perfectly normal. The position can sometimes affect emphasis or style, but here there is no major difference in basic meaning.

Because suus, -a, -um is the reflexive possessive adjective, used when the possessor is the subject of the clause.

Here the subject is una puella:

• Una puella ... scribit
• she writes in her own notebook

So Latin uses suo.

Very roughly:

• suus = his/her/its/their own
• eius = his/her/its, referring to someone else

So in commentario suo means in her own notebook.

It can mean either, depending on context.

Since Latin has no word for a/an, una can sometimes be used where English simply says a. But it can also keep its fuller sense of one.

So una puella may mean:

• a girl
• one girl

If the sentence is just introducing a character, English often translates it as a girl. If the writer wants emphasis on one single girl, then one girl is better.

You look for the accusative subjects and infinitives connected to scribit.

Here scribit governs two coordinated indirect statements:

1. senatum decreta facere
2. oratores autem in contione populum movere conari

The comma and autem help show the division, but both parts still depend on scribit.

So the whole thing is:

• A girl writes in her notebook [that the senate makes decrees], [but that the orators in the assembly try to move the people].

It is flexible, but not unusual.

Latin often puts the main verb fairly late and is happy to separate related words. Here the order is:

• Una puella = subject
• in commentario suo = where she writes
• scribit = main verb
• then the two indirect statements

Inside those indirect statements, the infinitives come at the end of their units:

• senatum decreta facere
• oratores autem in contione populum movere conari

That is very natural Latin style. English depends more on fixed word order; Latin depends more on endings.

It can definitely mean more than physical movement.

movere can mean:

• move physically
• stir
• affect
• arouse
• influence

With populum, especially in a political setting involving oratores and contio, it often suggests:

• stir up the people
• sway the people
• move the crowd emotionally

So the idea is probably rhetorical or political influence, not simply making people walk somewhere.