Learn Hardcore Croatian: Kad sam usamljen, zovem prijateljicu da mi pravi društvo. - When I am lonely, I call a female friend to keep me company.

kad – shorter, more colloquial, very common in speech and informal writing.
kada – a bit more formal or emphatic; common in writing, news, careful speech.

In this sentence, you can freely use either:

Kad sam usamljen, zovem prijateljicu…
Kada sam usamljen, zovem prijateljicu…

Both are correct; the difference is just style, not grammar.

Why is there no ja? Could I say Ja sam usamljen?

Croatian usually drops subject pronouns because the verb ending already shows the person.

Sam usamljen is impossible (you need the verb plus implied subject),
but Kad sam usamljen clearly means When I am lonely, because sam is 1st person singular of biti (to be).

You can add ja for emphasis:

Kad sam ja usamljen, zovem prijateljicu…
= When *I am lonely (as opposed to someone else), I call…*

Without emphasis, the most natural is to leave ja out, as in the original sentence.

Why is it usamljen and not something like usamljeno?

Usamljen is an adjective describing the subject ja (I):

(Ja) sam usamljen. – I am lonely.

The form usamljeno can function as:

neuter adjective (usamljeno dijete – lonely child), or
an adverb-like form: Osjećam se usamljeno – I feel lonely (literally: I feel in a lonely way).

In Kad sam usamljen, we’re saying I am lonely (adjective), not I feel lonely (adverb-like), so the correct form is usamljen.

Why is it usamljen (masculine) and not usamljena? What if the speaker is female?

Predicate adjectives must agree in gender and number with the subject.

For a male speaker:
Kad sam usamljen, zovem prijateljicu…
For a female speaker:
Kad sam usamljena, zovem prijateljicu…

Other forms:

plural mixed/masculine group: Kad smo usamljeni…
plural all-female group: Kad smo usamljene…

In isolation, grammar examples often use the masculine form as a “default”, but in real speech you change it to match who is speaking.

What is the dictionary form of zovem, and why is that form used here?

Zovem is 1st person singular present of zvati (imperfective).

infinitive: zvati – to call
present: zovem, zoveš, zove, zovemo, zovete, zovu

Croatian verbs come in aspect pairs:

zvati (imperfective) – ongoing/habitual actions
nazvati (perfective) – single, completed action (to call once, to have called)

In your sentence the action is habitual (whenever I’m lonely, I call), so the imperfective zovem is correct.

If you wanted to refer to a single, one‑off call, you’d use the perfective, often in future or past:

Kad budem usamljen, nazvat ću prijateljicu. – When I’m lonely (at that time), I’ll call her (once).

Why is it prijateljicu and not prijateljica?

Prijateljica is a feminine noun ending in -a.

In Croatian, such nouns change to -u in the accusative singular when they are direct objects:

nominative (who?): prijateljica
accusative (whom?): prijateljicu

Since zovem (I call) takes a direct object:

Zovem koga? – prijateljicu.

So prijateljicu is accusative singular feminine and is the correct form here.

Does prijateljicu mean specifically a female friend? How would I say a male friend?

Yes, prijateljica / prijateljicu clearly means female friend.

For a male friend, you use prijatelj:

nominative: prijatelj
accusative (animate masculine): prijatelja

So:

Zovem prijatelja. – I call a (male) friend.
Zovem prijateljicu. – I call a (female) friend.

The suffix -ica usually marks feminine forms of people nouns (učenik – učenica, prijatelj – prijateljica, etc.).

Should I say zovem svoju prijateljicu instead? When do I need svoju?

Svoju is the feminine accusative form of the reflexive possessive svoj = my/one’s own (referring to the subject).

Zovem prijateljicu. – I call a (the) friend (context says whose).
Zovem svoju prijateljicu. – I call my (own) friend.

In many everyday contexts, zovem prijateljicu is clear enough: people will assume it’s my friend if there is no other possessor in the context.

You must or should use svoju (or moju) when:

there could be ambiguity about whose friend it is, or
you want to emphasize that it’s my friend.

So both are grammatically correct; svoju just adds explicit possession:

Kad sam usamljen, zovem svoju prijateljicu… – perfectly fine and perhaps a bit clearer for learners.

What does mi mean in da mi pravi društvo, and is it necessary?

Mi here is the dative clitic of the 1st person singular pronoun (meni = to me).

So da mi pravi društvo literally is:

so that (she) makes company to me. → so that she keeps me company.

If you drop mi:

Zovem prijateljicu da pravi društvo.

This is grammatically possible but feels incomplete or vague: I call a friend so that she keeps company (to someone?)
Normally you specify to whom the company is made:

praviti nekome društvo – to keep someone company

So mi is natural and normally expected here. Without it, the sentence sounds off in everyday use.

Why is the verb pravi used? What does praviti društvo literally mean?

Pravi is 3rd person singular present of praviti (imperfective, colloquial) – literally to make or to do.

The expression praviti (nekome) društvo is an idiom meaning to keep (someone) company.

Literally:

praviti nekome društvo = to make company to someone.

Other possible variants:

činiti nekome društvo – same meaning, a bit more formal/neutral.
biti nekome društvo – to be company to someone.

In casual speech, praviti društvo is very common and sounds natural in this sentence:

…zovem prijateljicu da mi pravi društvo.

Why is it da mi pravi društvo and not an infinitive like praviti mi društvo?

Croatian very often uses da + present tense to express:

purpose: in order to…
or indirect commands / wishes / results.

Here, da mi pravi društvo is a purpose clause:

I call a friend *so that she keeps me company.*

Using the infinitive praviti mi društvo here would sound unnatural or wrong in standard Croatian. Purpose after verbs like ići, doći, zvati, etc., is normally expressed with da + present:

Dolazim da te vidim. – I’m coming to see you.
Zovem te da razgovaramo. – I’m calling you so that we talk.

So da mi pravi društvo is the standard, idiomatic form.

Why is the word order da mi pravi društvo and not da pravi mi društvo?

The short pronoun mi is a clitic. Croatian clitics follow (roughly) the “second position” rule: they must appear in the second position in the clause.

In this subordinate clause:

first word: da
second element: mi (the clitic)
then the main verb and the rest: pravi društvo

So:

da mi pravi društvo – correct and natural
da pravi mi društvo – ungrammatical in standard Croatian

Other acceptable word orders that still respect clitic placement:

Zovem prijateljicu da mi pravi društvo. – neutral
Zovem prijateljicu da mi društvo pravi. – possible, with slightly marked emphasis on društvo.

But mi must remain in that early, clitic position.

Is the comma after Kad sam usamljen necessary in Croatian?

Yes, according to standard rules, when a subordinate clause (like a kad-clause) comes before the main clause, you normally separate them with a comma:

Kad sam usamljen, zovem prijateljicu…

If you reverse the order, you usually drop the comma:

Zovem prijateljicu kad sam usamljen.

So the comma in your original sentence is standard and expected.