Ni havis nenian problemon.

-is is the Esperanto past-tense ending.

• havi = to have
• havis = had

So Ni havis... means We had...

The -n marks the direct object.

Here, problemon is the thing that was had, so it takes the accusative ending:

• Ni havis problemon = We had a problem

Esperanto often marks the direct object with -n, even when English does not show anything special.

Because nenian describes problemon, and adjective-like words in Esperanto must agree with the noun they modify.

Since problemon is:

• singular
• accusative

nenian must also be:

• singular
• accusative

So:

• nenia problemo = no problem
• nenian problemon = no problem, as a direct object

Nenian is the accusative singular form of nenia.

nenia means something like:

• no
• not any
• literally, often of no kind

Before a noun, it works much like an adjective:

• nenia problemo = no problem
• nenian problemon = no problem, as object

Because nenian already makes the sentence negative.

Esperanto usually does not add ne as well in a sentence like this. So the normal form is:

• Ni havis nenian problemon.

This already means We had no problem.

Yes. That is also correct.

• Ni ne havis problemon = We did not have a problem
• Ni havis nenian problemon = We had no problem

The meanings are very close.
Often, nenian problemon feels a bit more explicit or emphatic: absolutely no problem.

Because Esperanto can use the singular here just like English often does:

• no problem
• nenian problemon

If you wanted to stress multiple separate problems, you could use the plural:

• Ni havis neniajn problemojn. = We had no problems.

But the singular is very natural.

Esperanto has la for the, but it has no indefinite article like English a/an.

So:

• problemo can mean a problem
• la problemo means the problem

In this sentence, no definite article is needed, because it is not about one specific previously identified problem.

Yes. The normal order here is:

• Ni = subject
• havis = verb
• nenian problemon = object

So the basic order is subject–verb–object.

But because -n marks the object, Esperanto word order is fairly flexible. For emphasis, you could also say:

• Nenian problemon ni havis.

That still means the same thing, but puts extra focus on nenian problemon.

This is a very common question.

• nenia means no kind of / no
• neniu means no one / nobody / not a single one

Before a noun, both can sometimes appear, but they give slightly different shades of meaning:

• nenia problemo = no problem / no kind of problem
• neniu problemo = not a single problem

In a general sentence like this, nenian problemon is very natural and idiomatic.

It breaks down like this:

• Ni = we
• havis = had
• nenian = no
• problemon = problem, marked as the object

So the structure is:

• subject: Ni
• verb: havis
• direct object: nenian problemon

That is a very standard Esperanto sentence pattern.