Si soror iterum tussit, mater medicam statim vocabit.

Yes, that is a very common point of confusion.

Here tussit is present, not past. It is the 3rd-person singular present indicative of tussire/tussio, to cough. In verbs of this type, the present 3rd singular can end in -it, just like audit = he/she hears.

So here:

• tussit = she coughs
• not she coughed

The past/perfect of this verb is formed differently, such as tussivit or tussiit.

Because vocabit is the future tense of vocare, to call.

For many 1st-conjugation verbs, the future endings are:

• -bo
• -bis
• -bit
• -bimus
• -bitis
• -bunt

So:

• vocat = she calls
• vocabit = she will call

That -bit ending tells you it is 3rd-person singular future.

Because medicam is the direct object of vocabit.

Latin changes noun endings to show their job in the sentence. After a verb like vocare (to call), the person being called is in the accusative case.

So:

• medica = nominative, female doctor as subject
• medicam = accusative, female doctor as object

In this sentence, the mother is the one doing the calling, and the doctor is the one being called, so Latin uses medicam.

Because soror and mater are both subjects, while medicam is an object.

• soror is the subject of tussit
• mater is the subject of vocabit
• medicam is the object of vocabit

Also, soror and mater are 3rd-declension nouns, so their nominative singular forms do not look like -a nouns.

Compare:

• soror = subject

• sororem = object

• mater = subject
• matrem = object

So the forms are different because their grammatical roles are different.

Because Latin often uses exactly this pattern for a real, open condition:

• si
  • present
• main clause in the future

So Si soror iterum tussit, mater medicam statim vocabit means something like:

• If sister coughs again, mother will call the doctor immediately

English does the same thing:

• not usually If she will cough again, mother will call...
• but If she coughs again, mother will call...

So this structure is very natural in both languages.

Because Classical Latin has no articles.

So Latin often leaves it to context whether a noun should be understood as:

• a sister or the sister
• a mother or the mother
• a doctor or the doctor

In this sentence, English normally uses the or a possessive in translation, but Latin itself does not need a separate word for that.

No. Latin word order is much more flexible than English word order because the noun endings already show the grammatical roles.

This order is perfectly natural:

• Si soror iterum tussit, mater medicam statim vocabit.

But other orders are also possible, for example:

• Si soror iterum tussit, mater statim medicam vocabit.
• Mater medicam statim vocabit, si soror iterum tussit.

The basic meaning stays the same because:

• mater is still the subject
• medicam is still the object
• vocabit is still the verb

Word order in Latin often affects emphasis more than basic meaning.

They are both adverbs.

• iterum = again
• statim = immediately / at once

They modify the verbs:

• iterum goes with tussit: coughs again
• statim goes with vocabit: will call immediately

Because they are adverbs, they often have some freedom of position in the sentence.

Good question. Medica can function as an adjective, but it can also be used as a noun, meaning female doctor or female physician.

Here it is being used substantively, meaning simply doctor.

So in this sentence:

• medicam = the female doctor as a direct object

If the doctor were masculine, you would expect a form like medicum from medicus.

You can tell from both case and verb form.

First clause:

• soror is nominative, so it is the subject
• tussit is 3rd-person singular, matching soror

Second clause:

• mater is nominative, so it is the subject
• medicam is accusative, so it is the object
• vocabit is 3rd-person singular, matching mater

So the structure is:

• If sister coughs again
• mother will call the doctor immediately

Latin relies much more on endings than on position, so learning to spot nominative and accusative forms is very important.