Learn Farsi: گردشگر عوارض را پرداخت کرده، اسمش را در سیستم ثبت کرد. - The tourist paid the tax and registered his name in the system.

This is the clause chaining structure you are learning. Instead of using the word for 'and' (و) with two simple past verbs (پرداخت کرد و ثبت کرد), the first action is turned into a past participle (پرداخت کرده) without an auxiliary verb. Only the final verb (ثبت کرد) shows the tense and person.

How do you form the past participle for a compound verb like پرداخت کردن in these chains?

You keep the non-verbal part of the compound verb exactly the same (پرداخت) and only change the verbal part (کردن) into its past participle form (کرده). That gives you پرداخت کرده.

There are two را markers in this sentence. Do we always need a separate را for chained clauses?

Yes, if both verbs have their own specific, definite direct objects. Here, the tourist pays the tax (عوارض را) and registers his name (اسمش را). Since each action acts on a different definite object, each object needs its own marker.

What kind of tax does عوارض refer to here? Can I use it for income tax?

No, عوارض generally refers to tolls, municipal fees, or specific duties, like an exit tax or tourist fee. For general income or corporate taxes, you would use the word مالیات.