Ionako ćemo nastaviti.

Here ionako means anyway, in any case, or regardless.

So Ionako ćemo nastaviti. means something like:

• We’ll continue anyway.
• We’re going to continue regardless.

The word often adds a nuance like it doesn’t really matter what happened before; the result is the same.

This is the Serbian future tense.

It is built with:

• a form of hteti (to want) used as an auxiliary
• plus the infinitive of the main verb

Here:

• ćemo = we will
• nastaviti = to continue

So:

• ćemo nastaviti = we will continue

This is a very common way to form the future in Serbian.

Because Serbian often drops subject pronouns when they are already clear from the verb form.

In ćemo, the ending already tells you the subject is we.

So Serbian usually says:

• Ćemo nastaviti. = We will continue.

You could add mi for emphasis:

• Mi ćemo nastaviti.

That would sound more like:

• We will continue
  (as opposed to someone else)

Nastaviti is the infinitive form of the verb, meaning to continue.

Its basic dictionary form is:

• nastaviti = to continue

In this sentence, it comes after the future auxiliary ćemo, so it stays in the infinitive.

Nastaviti is generally treated as a perfective verb.

That means it often refers to a completed or bounded action, or to the act of resuming / continuing onward as a whole.

Its imperfective partner is usually:

• nastavljati

Very roughly:

• nastaviti = to continue / resume
• nastavljati = to be continuing / to continue repeatedly or over time

In a sentence like Ionako ćemo nastaviti, the perfective verb sounds natural because it refers to the decision or act of continuing.

Yes. With many verbs, Serbian can express the future in two ways:

• ćemo nastaviti
• nastavićemo

So you may also see:

• Ionako ćemo nastaviti.
• Nastavićemo ionako.

Both mean essentially the same thing.

However, Ionako ćemo nastaviti is a very natural way to say it, especially because ćemo behaves like a clitic and often appears near the beginning of the sentence.

Because ćemo is a clitic in Serbian.

Clitics are short unstressed words that usually cannot stand freely in just any position. They often appear in the second position of the sentence or clause.

So in:

• Ionako ćemo nastaviti.

the first element is ionako, and the clitic ćemo comes right after it.

This is a very normal Serbian word-order pattern.

They are similar, but not always identical.

• ionako = anyway / regardless / as it is
• u svakom slučaju = in any case
• svejedno = it’s all the same / anyway / no difference

In this sentence, ionako suggests something like:

• No matter what, we’ll continue
• We were going to continue anyway

So it can carry a slightly stronger sense of regardless of the circumstances.

It often sounds a bit like:

• We’ll continue no matter what
• We were going to continue anyway
• That doesn’t change the fact that we’ll continue

Depending on context, it can sound:

• determined
• dismissive
• matter-of-fact
• slightly stubborn

So the exact tone depends on who says it and why.

The tricky sound is ć.

• ć is a soft sound, somewhat like the t in British English tune for some speakers, or a very soft ch/t sound.
• ćemo is roughly pronounced CHYEH-mo, but that is only an approximation.

Also note:

• č and ć are different sounds in Serbian
• ć is softer than č

So:

• ćemo is not the same as čemo

Yes:

• Mi ćemo nastaviti.

That is grammatically correct. But adding mi usually gives extra emphasis.

Compare:

• Ćemo nastaviti. / Ionako ćemo nastaviti.
  neutral
• Mi ćemo nastaviti.
  we will continue, perhaps not someone else

In most everyday contexts, Serbian does not need the pronoun unless there is contrast or emphasis.