Ja, ik ben er nu mee bezig, maar eerst moet ik op het juiste icoon klikken.

It uses the fixed expression bezig zijn met = to be busy with / to be working on.

So:

• ik ben bezig met ... = I am working on ...
• ik ben er nu mee bezig literally = I am busy with it now

In natural English, that often becomes Yes, I’m working on it now or Yes, I’m dealing with it now.

This is a very common Dutch pattern: a preposition + pronoun often becomes a pronominal adverb.

Because the full pattern is:

• bezig met iets = busy with something

If iets becomes it, Dutch usually does not say met het here. Instead it uses:

• er ... mee

So:

• Ik ben met het werk bezig = I’m busy with the work
• Ik ben ermee bezig = I’m busy with it

Here the speaker has inserted nu, so ermee gets split:

• Ik ben er nu mee bezig

That split is normal.

Because ermee can be split when another element is placed in between, especially an adverb like nu.

So both ideas are related:

• Ik ben ermee bezig
• Ik ben er nu mee bezig

Dutch often allows the er part and the preposition part (mee) to separate. This happens a lot in real sentences.

Yes, that is possible, but Ik ben er nu mee bezig sounds more natural and idiomatic to many speakers.

Dutch often prefers to keep er earlier in the clause and leave the preposition part (mee) closer to the adjective or verb it belongs to.

So the given sentence is a very good, natural model to learn from.

Nu is an adverb meaning now, and Dutch adverbs can move around more than in English.

In this sentence:

• ik ben er nu mee bezig

nu sits in the middle of the verbal expression and sounds very natural there.

You could also hear:

• Ik ben nu ermee bezig
• Ik ben er mee bezig nu (less natural in many contexts)

The given word order is one of the most standard ways to say it.

In a main Dutch clause, the finite verb usually comes in second position. This is the famous V2 rule.

Here the clause begins with eerst:

• eerst = first
• then the finite verb moet
• then the subject ik

So:

• maar eerst moet ik ...

This is correct Dutch word order.

You could also say:

• maar ik moet eerst ...

That is also correct, but the emphasis is slightly different.
The original sentence highlights first more strongly.

Because moeten is a modal verb.

With a modal verb in a main clause, Dutch usually places:

• the finite modal verb earlier: moet
• the main verb in the infinitive at the end: klikken

So:

• ik moet klikken = I must click
• eerst moet ik op het juiste icoon klikken

That final infinitive position is completely normal in Dutch.

Because the verb klikken in the sense of clicking a button or icon is normally used with op:

• op een knop klikken = click on a button
• op een link klikken = click on a link
• op het icoon klikken = click on the icon

This works much like English click on, although in modern English people also often just say click the icon. In Dutch, op is the standard choice here.

juist can mean correct, right, or proper, depending on context.

So:

• het juiste icoon = the correct/right icon

Here it means the icon that is the one you need, not the wrong one.

Because juiste is an adjective before a noun, and in Dutch adjectives usually take -e when they come before a noun with a definite article.

Here:

• het icoon = the icon
• definite article = het
• adjective before the noun = juiste

So:

• het juiste icoon

Even though icoon is a het-word, you still use -e here because the noun is definite.

Compare:

• een juist antwoord = a correct answer
• het juiste antwoord = the correct answer

It is a het-word:

• het icoon

That is why the sentence says:

• op het juiste icoon

Learners often want to memorize new nouns together with their article, so it is useful to learn het icoon as a set.

No. It is very broad and can refer to almost any task, project, or activity.

For example:

• Ik ben ermee bezig. = I’m working on it.
• We zijn er nog mee bezig. = We’re still dealing with it.
• Ben je er al mee bezig? = Are you working on it already?

So in your sentence, er does not refer to the icon. It refers to the task or issue the speaker is working on.
The icon appears later as the next step: first I have to click on the right icon.

Yes, sometimes daarmee is possible, but it is not exactly the same in feel.

• ermee often means with it in a general, unstressed way
• daarmee can sound a bit more specific or contrastive, like with that

So:

• Ik ben ermee bezig = I’m working on it
• Ik ben daarmee bezig = I’m working on that / with that

In your sentence, er ... mee is the most neutral and natural choice.