Na kraju razgovora zagrlili smo jedno drugo i više nije bilo problema.

Because na kraju is a fixed expression meaning at the end, and kraj then takes the genitive case.

So the structure is:

• na kraju = at the end
• razgovora = of the conversation

That is why razgovor changes to razgovora. The whole phrase means at the end of the conversation.

Croatian does not have articles like English the and a/an.
So nouns like razgovora and problema appear without any separate word for article.

English has to choose:

• the conversation
• a problem / problems

Croatian leaves that to context.

It is the Croatian past tense, made from two parts:

• zagrlili = past participle of zagrliti
• smo = we are / we have as the auxiliary used to form the past tense

Together, zagrlili smo means we hugged.

A very common Croatian past-tense pattern is:

• radio sam = I worked
• došli smo = we came
• zagrlili smo = we hugged

Because in Croatian, the past participle agrees with the subject in number and gender.

• zagrlili smo = we hugged, if the group is masculine or mixed
• zagrlile smo = we hugged, if the speakers are all female

So this sentence uses the masculine plural form, which is also the normal form for a mixed group.

Because Croatian often leaves subject pronouns out when the verb already shows who the subject is.

Here smo already tells you the subject is we.

So:

• zagrlili smo = we hugged
• mi smo zagrlili = we hugged, with extra emphasis on we

This omission of subject pronouns is very common in Croatian.

This is a normal Croatian word order in the past tense. The auxiliary smo is a clitic, and clitics have special placement rules.

For learners, the most useful thing to remember is simply that forms like these are standard and very common:

• vidio sam
• došli smo
• zagrlili smo

Croatian word order is flexible, so you may also see other arrangements in different contexts, but zagrlili smo is completely natural.

It means each other or one another.

So:

• zagrlili smo jedno drugo = we hugged each other

Croatian often uses expressions based on jedan / jedna / jedno plus drugi / druga / drugo to express reciprocity.

In this sentence, it is best to understand jedno drugo as an idiomatic reciprocal expression.

Yes. Zagrlili smo se is also very natural, and in everyday speech it may even be more common.

The difference is roughly this:

• zagrlili smo se = we hugged
• zagrlili smo jedno drugo = we hugged each other

The version with jedno drugo is more explicit and can sound a bit more deliberate or emotionally emphatic.

Here više means anymore or no longer, not just the comparative more.

So:

• više nije bilo problema = there were no more problems
• više nije bilo problema = there were not any problems anymore

This is a very common use of više together with negation.

Because this is an impersonal existential construction.

Croatian often says:

• bilo je = there was / there were
• nije bilo = there was not / there were not

In this pattern, Croatian uses bilo, the neuter singular form, even when English would use were.

So:

• Bilo je problema. = There were problems.
• Nije bilo problema. = There were no problems.

Because after bilo je / nije bilo in this existential meaning, Croatian commonly uses the genitive.

So:

• bilo je problema
• nije bilo problema

That is why the noun appears as problema.

Also, with the noun problem, the form problema looks the same in both genitive singular and genitive plural. In this sentence, the meaning is clearly plural or general: no more problems.

Because zagrliti is perfective, so it presents the action as one completed event.

That fits this sentence well: at the end of the conversation, the hug happened as a single completed action.

Compare:

• zagrlili smo = we hugged
• grlili smo = we were hugging / we hugged repeatedly

So zagrlili smo is the natural choice here.