Learn Hardcore Hausa: A lokacin da nake danna lambar sirri, ina kallon agogo in ga lokacin da na ɗauka. - When I am pressing the PIN, I look at the watch to see how much time I take.

You can say Lokacin da nake danna lambar sirri… without the a. The meaning is practically the same. The version with a just makes the “at (that) time” idea a bit more explicit, but both are very natural.

Why is it da nake danna and not da ina danna?

Hausa uses two different progressive patterns, and which one you use depends on the environment:

Main clause progressive
Use ina / kana / yana / tana / muna… + verbal noun:
- Ina kallon agogo. – I am looking at the clock.
Relative / “when” / “while” clause (after da)
Use [subject pronoun] + ke + verb:
- da nake danna – when I am pressing / while I’m pressing
  - na + ke → nake (1st person singular)
- da yake tafiya – when he is going

So after da, you don’t normally say da ina danna; you use da nake danna. That’s why the sentence is:

A lokacin da nake danna lambar sirri…
At the time when I am pressing the PIN…

What is the role of da in lokacin da nake… and lokacin da na ɗauka?

Here da is a relativizer / linker, roughly “that / when” in English.

lokacin da nake danna lambar sirri
→ the time *when I am pressing the PIN*
lokacin da na ɗauka
→ the time *that I took (used up)*

So:

lokacin = time
lokacin da … = the time that / the time when …

Note that da can also mean and, with, using in other contexts, but here it is purely a clause linker.

How is lambar sirri put together, and does it literally mean “PIN”?

Lambar sirri is a genitive (possessive-like) noun-noun phrase:

lamba – number
-r – linking suffix (genitive marker)
sirri – secret (noun)

So literally it is “number of secret” → “secret number”, which is the normal Hausa way to say PIN code.

Some points:

It functions just like English “secret number”.
You might also see things like lambar waya (phone number), lambar awo (measurement number), etc. Same pattern.

Why is it ina kallon agogo, with kallon, and not something like ina kalle agogo?

In ina kallon agogo, Hausa is using the progressive with a verbal noun:

ina – I am (doing…)
kallo – a look, act of looking (verbal noun of kalli “to look at/watch”)
kallo + -n + agogo → kallon agogo – a look of/at the clock

So ina kallon agogo is literally “I am (in) the act of-looking-of clock”, i.e. I am looking at the clock.

You don’t say *ina kalle agogo. The “ina” progressive wants a verbal noun, not the basic finite verb. A few more parallels:

ina karatun littafi – I am reading a book (karatu “reading/study”)
ina cin abinci – I am eating food (ci → cin “eating”)
ina kallon fim – I am watching a film (kallo → kallon)

In ina kallon agogo in ga…, what does in mean? Is it “if” or “to / in order to”?

Here in introduces a subjunctive-like clause and means roughly “to / in order to / so that I can”, not “if”.

ina kallon agogo in ga…
→ I’m looking at the clock *to (so that I can) see …*

This is the same in you find in very common patterns like:

Na zo in ganka. – I came to see you.
Zan je kasuwa in sayi nama. – I’ll go to the market to buy meat.

So in this sentence in ga = “(so that) I see”, i.e. to see.

Why is it in ga and not in gani?

The verb “to see” is a bit irregular:

ga – finite verb form (see)
gani – verbal noun (seeing, sight)

With in (which takes a finite verb), you use ga, not the verbal noun:

in ga lokacin… – to see the time… (correct)
*in gani lokacin… – ungrammatical in this structure

Compare:

Zan ga shi gobe. – I’ll see him tomorrow.
Ina gani. – I see / I’m seeing. (here gani is used with ina as a verbal noun)

So:

ina gani – progressive + verbal noun
in ga – “to/so that I see” + finite verb

What exactly does lokacin da na ɗauka mean? Where is the object of ɗauka?

ɗauka literally means “to take, to pick up”, but with lokaci / lokaci it is used idiomatically for “to take (time)”.

In lokacin da na ɗauka:

lokacin – the time
da – that / which
na ɗauka – I took (it)

The object of na ɗauka is actually lokacin itself, but it’s understood through the relative construction:

literally: “the time that I took”
idiomatically: “the time it took me / the time I used (up)”

So the whole ending:

…in ga lokacin da na ɗauka.
→ …to see the time that I took (the time it took me).

Could I say tsawon lokacin da na ɗauka instead of lokacin da na ɗauka?

Yes, and it would sound very natural and a bit clearer:

tsawo – length
tsawon lokaci – length of time, duration

So:

tsawon lokacin da na ɗauka
→ the length of time that I took / the duration it took me

Your sentence could become:

…ina kallon agogo in ga tsawon lokacin da na ɗauka.
→ …I look at the clock to see how long it took me.

lokacin da na ɗauka is understood in context, but tsawon lokacin da na ɗauka makes the “duration / how long” idea more explicit.

Are nake danna and ina kallon both present progressive? Why use two different forms in one sentence?

Yes, both express an ongoing action, but they appear in different syntactic environments, so different forms are required:

A lokacin da nake danna lambar sirri…
- inside a “when/while” relative clause (after da)
- so Hausa uses [subject] + ke + verb → nake danna
…ina kallon agogo…
- this is the main clause
- so Hausa uses ina + verbal noun → ina kallon

So:

nake danna – progressive inside the da-clause
ina kallon – progressive in the main clause

Both can refer to a habitual present (what you normally do), just like English “When I’m entering my PIN, I look at the clock…” where English also uses present progressive for a repeated/habitual action.