Mihi hodie satis temporis non est, sed sorori meae est, et illa matri in agro auxilium dat.

Because mihi is the dative singular of ego, and Latin often uses the dative with est to express possession or availability.

So:

• Mihi ... non est = literally to me ... is not
• natural English: I do not have ...

In this sentence, Mihi hodie satis temporis non est literally means something like To me today there is not enough time.

This is a very common Latin way to say I have / I do not have something.

For the same reason as mihi.

The second clause is:

• sed sorori meae est

Literally: but to my sister there is

The idea is still there is enough time for my sister or more naturally my sister has enough time.

So both mihi and sorori meae are datives because they show the person to whom something is available / belongs.

Because satis commonly takes the genitive to show enough of something.

So:

• satis temporis = enough time
• literally: enough of time

Here temporis is the genitive singular of tempus.

This is a pattern worth remembering:

• satis pecuniae = enough money
• satis aquae = enough water
• satis temporis = enough time

Yes. It is very normal Latin.

Latin often does not say possession the same way English does. Instead of using a verb exactly like English have, Latin often says:

• to me there is
• to me there is not

So:

• Mihi est = I have
• Mihi non est = I do not have

With satis temporis, that becomes:

• Mihi satis temporis est = I have enough time
• Mihi satis temporis non est = I do not have enough time

Latin could sometimes leave it out, but repeating est makes the contrast clear and neat:

• Mihi hodie satis temporis non est
• sed sorori meae est

The second clause leaves out satis temporis because it is understood from the first clause, but it keeps est to complete the statement.

So the full sense is:

• I do not have enough time today, but my sister does.

This is similar to English, where we also often say I don’t, but she does.

Yes, Latin often can leave the subject out, because the verb ending usually tells you the person. But here the verb is dat, which only tells you he/she/it gives, not which person exactly.

So illa is useful for clarity:

• illa = she

It can also add a little emphasis, like that woman / she.

Here it makes it clear that the sister is the one helping:

• et illa ... dat = and she gives ...

Without illa, the sentence would still be possible, but the explicit pronoun helps the reader follow who is doing the action.

Because dare takes:

• a direct object = the thing given
• an indirect object in the dative = the person receiving it

Here:

• auxilium = the thing given
• matri = the person receiving it

So:

• matri auxilium dat = she gives help to her mother

This is exactly the same basic idea as English give help to someone.

Yes. Auxilium dare is a standard Latin expression meaning to give help or simply to help.

So:

• auxilium dat = she gives help
• natural English: she helps

Also, auxilium is singular here because it works like a mass noun: help rather than helps.

Because in with the ablative usually means in or on, showing location.

So:

• in agro = in the field, on the farm

If Latin used in + accusative, that would usually suggest motion into something:

• in agrum = into the field

Here no movement is being described; the mother is located there. So in agro is the right form.

Because Latin often leaves out a possessive pronoun when it is already obvious from the context.

Earlier, the sentence mentioned sorori meae = my sister. Then it says:

• et illa matri in agro auxilium dat

Since illa refers back to my sister, matri will naturally be understood as to her mother or, in the context of the whole sentence, to our/my mother, depending on how the sentence is being interpreted.

Latin is often less explicit than English about possessives when the relationship is clear.

Because Latin word order is much more flexible than English word order. The endings show each word’s role, so Latin does not depend as heavily on position.

For example:

• Mihi hodie satis temporis non est
• literally ordered: To me today enough time not is

But the cases and verb make the meaning clear.

Latin writers often arrange words for:

• emphasis
• contrast
• rhythm
• style

In this sentence, the order highlights the contrast nicely:

• mihi ... non est
• sed sorori meae est

So the structure helps you feel: I don’t have enough time today, but my sister does.

Hodie is an adverb meaning today. It modifies the whole idea of having enough time.

So the sense is:

• Today, I do not have enough time

It does not change the noun temporis by itself; rather, it tells you when the statement is true.

Yes. Ille, illa, illud can be:

• a demonstrative adjective: that
• a demonstrative pronoun: that one
• sometimes, in context, simply he/she/it

Here illa most naturally means she, referring back to the sister. But it still has a slightly more pointed feel than an omitted subject, almost like that one or that girl / woman depending on context.

So the force is something like:

• and she / and that one

In ordinary translation, she is best.