После ссоры нам было трудно снова говорить друг с другом.

Because после always takes the genitive in Russian.

• ссора = an argument, quarrel
• после ссоры = after the argument / after the quarrel

So ссоры is the genitive singular form of ссора.

This is a very common Russian pattern: a dative experiencer plus an impersonal predicate.

• нам = to us
• было трудно = was difficult

So the structure is literally something like To us, it was difficult...

Russian often uses this instead of making we the grammatical subject. It sounds natural for feelings, states, and situations:

• мне холодно = I am cold
• ему интересно = he is interested / it is interesting to him
• нам было трудно = it was hard for us

Because this is an impersonal sentence in the past tense.

In the present tense, Russian usually says:

• нам трудно = it is hard for us

In the past tense, Russian adds было:

• нам было трудно = it was hard for us

It is neuter singular because there is no real subject controlling agreement. That is the normal default form in impersonal past-tense constructions.

Because трудно is not describing a noun here. It is being used as a predicative word meaning difficult/hard in the sense of a state or situation.

• трудный разговор = a difficult conversation
  Here трудный is an adjective modifying the noun разговор.

• нам было трудно говорить = it was hard for us to talk
  Here трудно describes the situation, not a noun.

So after an infinitive like говорить, Russian normally uses трудно, not трудный.

After words like трудно, легко, интересно, приятно, Russian often uses an infinitive to say what is difficult, easy, interesting, pleasant, and so on.

So:

• трудно говорить = hard to talk
• легко понять = easy to understand
• интересно читать = interesting to read

In this sentence, говорить names the action that was difficult.

Because the sentence is talking about the process or activity of talking again, not one single completed utterance.

говорить is imperfective, so it fits the idea of ongoing interaction or conversation.

If you used a perfective verb such as сказать, it would sound more like to say something once, which is not the idea here.

So:

• говорить = to talk, to speak, to be talking
• сказать = to say, to say once, to make a single statement

Here the meaning is clearly about resuming communication, so говорить is the natural choice.

Yes, absolutely.

• нам было трудно снова говорить друг с другом
• нам было трудно снова разговаривать друг с другом

Both are natural.

The difference is small:

• говорить is broader and can mean to speak / to talk
• разговаривать more clearly emphasizes having a conversation

In this sentence, разговаривать might sound slightly more explicitly like talking with each other, but говорить is still perfectly good Russian.

Yes, опять could work too.

• снова = again, anew
• опять = again

Very often they overlap. But снова can sound a bit more neutral or a bit more like once again / anew, while опять can sometimes carry a slight feeling of again... in an annoyed sense, depending on context and intonation.

In this sentence, снова fits nicely because it suggests resuming communication after a break.

Because the form of each other changes depending on the grammar of the sentence.

Here the verb pattern is:

• говорить с кем? = to talk with whom?

That requires с + instrumental. So Russian says:

• друг с другом = with each other

But in another sentence, a different form may be needed:

• они видят друг друга = they see each other

There, no с is used, and the grammar calls for друг друга instead.

So друг с другом is not random—it matches the structure required by говорить с кем-то.

It is instrumental singular.

That is because с in the sense of with normally takes the instrumental:

• с братом = with a brother / with my brother
• с другом = with a friend
• друг с другом = with each other

This expression is a set pattern:

• first part: друг
• second part after с: другом

So the second word changes because of the preposition.

No, Russian word order is flexible, but the given order is very natural.

• После ссоры sets the time/context first.
• нам было трудно gives the main state.
• снова говорить друг с другом tells us what was difficult.

So the sentence flows naturally from context to feeling/state to action.

You could rearrange it for emphasis, for example:

• После ссоры снова говорить друг с другом нам было трудно.

This is still correct, but it sounds a bit more marked or literary. The original order is the most neutral.