Puella digitum ostendit et dicit spinam parvam in eo fuisse, sed matrem eam statim tulisse.

Because digitum is the direct object of ostendit: the girl shows her finger.

• digitus = finger
• digitum = finger, as the object of the verb

So Puella digitum ostendit means The girl shows her finger.

It can be either in form:

• present: he/she shows
• perfect: he/she showed

That is a common feature of some 3rd person singular Latin verbs. Context has to decide.

Here, because it is followed by et dicit and the sentence feels vivid and immediate, learners will often take it as present: The girl shows ... and says ...

Because Latin normally does not use a separate word like English that after verbs of saying, thinking, knowing, and so on.

Instead, Latin uses indirect statement, usually with:

• an accusative subject
• an infinitive verb

So instead of saying she says that a small thorn was in it, Latin says:

• dicit
• spinam parvam ... fuisse

Literally, that is something like she says a small thorn to have been in it, but in normal English we translate it as she says that a small thorn was in it.

Because in a Latin indirect statement, the subject of the infinitive goes into the accusative.

So:

• direct statement: spina parva in eo fuit = a small thorn was in it
• indirect statement: dicit spinam parvam in eo fuisse = she says that a small thorn was in it

Here spinam parvam is the subject of fuisse, but in indirect statement that subject is accusative.

Because fuisse is the perfect infinitive of esse, and it shows action earlier than the time of dicit.

Latin infinitives in indirect statement show relative time:

• present infinitive = same time as the main verb
• perfect infinitive = earlier than the main verb
• future infinitive = later than the main verb

So:

• dicit spinam parvam in eo esse = she says that a small thorn is in it
• dicit spinam parvam in eo fuisse = she says that a small thorn was / had been in it

Since the thorn was there before she speaks, fuisse is correct.

in eo means in it or in him depending on context. Here it means in it, referring to digitum.

Why eo?

• it comes from is, ea, id
• eo is ablative singular masculine or neuter
• it refers back to digitum, which is masculine

Also, in with the meaning in/on for location takes the ablative:

• in eo = in it

So eo is masculine singular ablative because it refers to digitum and follows in of location.

Because in can take different cases depending on meaning:

• in + accusative = motion into, onto
• in + ablative = location in, on

Here the thorn was in the finger, not going into the finger. So Latin uses the ablative:

• in eo = in it

If it were motion into something, then accusative would be used.

For the same reason that spinam parvam is accusative: matrem is the subject of an infinitive inside indirect statement.

The second part depends on the same dicit:

• dicit ... matrem eam statim tulisse

So Latin is saying:

• she says that her mother took it away immediately

Since matrem is the subject of tulisse in indirect statement, it appears in the accusative.

It refers to spinam, the thorn.

You can tell by gender and case:

• spina is feminine singular
• eam is feminine singular accusative

So eam = it, meaning the thorn.

It cannot refer to digitum, because digitus is masculine. If it referred to the finger, we would expect eum.

tulisse is the perfect infinitive of ferre.

Its basic idea is to have carried or to have taken. In this context, it means something like to have taken away / removed.

So:

• matrem eam statim tulisse = that her mother removed it immediately

Again, the perfect infinitive shows that this action happened before the time of dicit.

Because both infinitive clauses depend on the same dicit.

The structure is:

• Puella ... dicit
• spinam parvam in eo fuisse
• sed matrem eam statim tulisse

So Latin is effectively saying:

• The girl says [that a small thorn was in it], but [that her mother took it away immediately].

Latin often leaves the governing verb understood when two parallel parts are joined by et, sed, and similar conjunctions.

Yes. If you turn the indirect statement into direct speech, the accusatives and infinitives become normal finite clauses.

Indirect:

• dicit spinam parvam in eo fuisse, sed matrem eam statim tulisse

Direct:

• spina parva in eo fuit, sed mater eam statim tulit

That helps show what Latin has changed:

• spina parva → spinam parvam
• mater → matrem
• fuit → fuisse
• tulit → tulisse

Those are the normal changes when Latin turns a statement into indirect statement after dicit.