Na mayar da takalmin duk da ragin.

Na marks 1st person singular in the completive/perfective. In natural English, Na mayar... is usually translated as I returned... or I have returned....

So the sentence begins with the idea I did / I have done.

Yes. It is very helpful to learn mayar da as a set pattern.

With an object after it, mayar da commonly means things like:

• return
• take back
• put back

So here, mayar da takalmin means return the shoe / take the shoe back / put the shoe back, depending on context.

No. They are doing different jobs.

• The first da in mayar da takalmin belongs to the verb pattern mayar da.
• The second da in duk da ragin is part of the fixed expression duk da, which means despite / in spite of.

So even though the same word da appears twice, it is not functioning the same way both times.

The basic form is takalmi, meaning shoe.

Takalmin is a different form of that same noun, used in a linked/definite type of environment. In this sentence, it is best understood as a specific shoe, roughly the shoe.

That -n is part of a common Hausa noun pattern. Many nouns change form when they are in a linked or definite/specific environment.

So:

• takalmi = shoe
• takalmin = a linked/definite form, often corresponding to the shoe in context

This is one reason English speakers often feel that Hausa is hiding the word the inside the noun form rather than using a separate article.

It is singular.

• takalmi = shoe
• takalma = shoes

So takalmin is the singular linked/definite form. If you wanted the shoes, you would normally expect a plural form based on takalma, often takalman in a linked/definite environment.

Usually not in the way English does.

Hausa often shows definiteness through:

• the form of the noun itself
• context
• demonstratives such as nan or can

So instead of a separate word exactly like English the, Hausa often lets forms like takalmin and ragin carry that sense.

Duk da is a fixed expression meaning despite or in spite of.

It is best learned as a chunk. A very literal word-for-word approach is not especially helpful here. In this sentence:

• duk da ragin = despite the discount

So if you see duk da, think despite / even with / in spite of.

The basic form is ragi.

Ragi can mean:

• reduction
• decrease
• discount

In this sentence, it means the discount. Just like takalmin, the form ragin shows that linked/definite -n ending.

So:

• ragi = discount, reduction
• ragin = the discount / the reduction

Because that is a very natural Hausa word order.

The sentence is basically:

• Na mayar da takalmin = I returned the shoe
• duk da ragin = despite the discount

Hausa often puts this kind of extra phrase after the main verb phrase. So the end position here is normal and unmarked.

Yes.

Because na marks a completed action, English may translate it as either:

• I returned the shoe
• I have returned the shoe

The right choice depends on the wider context. English forces you to choose a tense more explicitly than Hausa does here.

No. For an ongoing action, you would normally use a different marker, not na.

Here na shows a completed action. So this sentence is not naturally understood as I am returning.... It is understood as something already done: I returned / I have returned...