Ina duba takalmi yayin da abokina yake duba tambari.

Yes, roughly. In this kind of sentence, ina marks first person singular and an ongoing action, so Ina duba... means I am looking... or I am checking....

Hausa does not need a separate word exactly like English am here.

In this sentence, it means I am looking or I am checking, because the action is happening at that time.

Depending on context, Hausa forms like this can sometimes overlap with broader present-time meaning, but here the presence of yayin da and the parallel second clause strongly suggest an ongoing action: I am looking ... while my friend is looking ...

Yayin da means while or sometimes when, depending on context.

In this sentence, it means while, because it connects two actions happening at the same time:

• Ina duba takalmi = I am looking at the shoe
• yayin da abokina yake duba tambari = while my friend is looking at the label/logo/mark

Treat yayin da as one connector here, not as separate words you need to translate one by one.

Because Hausa often adds possession directly to the noun.

• aboki = friend
• abokina = my friend

So the ending -na means my here.

Because after a connector like yayin da, Hausa commonly uses a subordinate/relative form of the continuous marker.

So:

• standalone main clause: Abokina yana duba tambari.
• after yayin da: ...abokina yake duba tambari.

That change from yana to yake is a normal grammar pattern in Hausa subordinate clauses.

Because Hausa duba usually takes its object directly.

English says:

• look at the shoe

Hausa says:

• duba takalmi

So duba takalmi naturally means look at the shoe or check the shoe, even though there is no separate word for at.

Hausa does not use articles the same way English does.

So takalmi can be understood from context as something like:

• a shoe
• the shoe

and tambari can similarly be understood from context.

English requires an article more often; Hausa often does not.

It can mean several related things, depending on context: mark, emblem, logo, label, stamp, brand sign.

So if the meaning shown to you uses one of those English words, that is normal. Hausa tambari is a fairly broad word.

Because Hausa normally states the verb in each clause clearly.

So this is natural:

• Ina duba takalmi yayin da abokina yake duba tambari.

That is more explicit and more normal than trying to leave the second duba understood.

A simple way to break it down is:

• Ina = I am
• duba = looking at / checking
• takalmi = shoe
• yayin da = while
• abokina = my friend
• yake = is
• duba = looking at / checking
• tambari = label/logo/mark

So the pattern is basically:

[first clause] + while + [second clause]

More literally:

I am looking at a/the shoe while my friend is looking at a/the label/logo.

Yes, Hausa has other ways to express similar ideas, such as sa’ad da or lokacin da in some contexts.

But yayin da is perfectly good and natural here. For a learner, it is a very useful expression to know for while.