Mater respondet se palla veteri adhuc uti posse, sed soleas novas emendas esse.

Because respondet introduces an indirect statement. In Latin, the subject of an indirect statement normally goes into the accusative, so ego becomes se when the speaker is referring back to herself.

Here, se refers back to Mater:

• Mater respondet = Mother replies
• se ... posse = that she can ...

So se means herself / she, referring to the mother.

Latin usually does not use a separate word like English that in this kind of sentence. Instead, it uses the accusative-and-infinitive construction:

• se ... posse
• soleas novas emendas esse

So where English says she replies that..., Latin simply uses an accusative subject plus an infinitive.

Uti is the infinitive of utor.

That is needed because posse means to be able, and it normally takes an infinitive:

• uti posse = to be able to use

If the clause were direct, you might have a finite verb such as utor or utitur depending on the sentence. But in indirect statement after respondet, Latin uses infinitives.

Also, utor is a deponent verb: it has passive-looking forms but an active meaning. So uti still means to use, not to be used.

Because utor is one of the Latin verbs that takes an ablative object.

So:

• palla veteri uti = to use an old cloak
• literally, something like to make use of an old cloak

That is why you do not get an accusative like pallam veterem here.

In ordinary spelling without macrons, palla can look the same in the nominative and ablative singular. With macrons, the ablative would be pallā.

We know it is ablative here because:

• utor / uti requires the ablative
• veteri is clearly ablative singular, and the adjective must agree with palla

So the phrase is pallā veterī in full marked spelling.

Because posse needs an infinitive to complete its meaning.

• posse = to be able
• uti = to use

Together:

• uti posse = to be able to use

This is very common in Latin, just like English to be able to use has two verb forms.

Adhuc here means still.

So:

• palla veteri adhuc uti posse = to still be able to use the old cloak

It shows that the cloak is not yet worn out beyond use.

Because it is the subject of the infinitive esse inside an indirect statement.

In English, we would say:

• that new sandals must be bought

There, new sandals is the subject.

In Latin indirect statement, that subject becomes accusative, so:

• direct: soleae novae emendae sunt
• indirect: soleas novas emendas esse

So soleas novas is not a direct object here; it is the accusative subject of esse.

Emendas esse is a gerundive of obligation (also called the passive periphrastic).

It means:

• to have to be bought
• to need to be bought
• must be bought

So:

• soleas novas emendas esse = that new sandals must be bought

Also, emendas here is from emere = to buy, not from emendare.

Because emendas is a verbal adjective agreeing with soleas novas.

All three words match:

• soleas = feminine plural accusative
• novas = feminine plural accusative
• emendas = feminine plural accusative

That agreement is required because the gerundive behaves like an adjective.

Because the second clause does not explicitly say who must buy the sandals. It simply says that the sandals need to be bought.

Latin can leave the responsible person unstated. If you wanted to say specifically that she must buy new sandals, Latin could add a dative of agent, for example:

• sibi soleas novas emendas esse

That would mean more specifically that new sandals have to be bought by her.

As written, the sentence is a little more general: but new sandals must be bought.

Because they are agreeing with different nouns in different grammatical roles.

• veteri agrees with palla
  
  • ablative singular feminine
  • because utor takes the ablative
• novas agrees with soleas
  
  • accusative plural feminine
• emendas also agrees with soleas
  
  • accusative plural feminine

So the different endings are not random; they reflect different cases and numbers.

A likely direct version would be:

• Pallā veterī adhūc ūtī possum, sed soleae novae emendae sunt.

That means:

• I can still use the old cloak, but new sandals must be bought.

Then after Mater respondet, Latin changes it into indirect statement:

• possum → posse
• soleae novae emendae sunt → soleas novas emendas esse
• the speaker I becomes se, referring back to Mater

No. Latin word order is fairly flexible because the endings show the grammar.

So the sentence could be rearranged in other ways without changing the basic meaning, for example:

• Mater respondet se adhuc palla veteri uti posse...
• Mater se palla veteri adhuc uti posse respondet...

The given order is natural and helps the sentence flow:

• first, what the mother says about the old cloak
• then, after sed, the contrast about the sandals