Learn Hardcore Icelandic: Ég geri pöntun á netinu og fæ staðfestingu strax. - I make a reservation online and get a confirmation immediately.

Yes. Að panta (to order) is very common and concise: Ég panta á netinu. The noun + verb collocations gera pöntun and especially leggja inn pöntun (“place an order”) are also natural, often in business or formal contexts. All are fine; for everyday speech, panta is the simplest.

Why is it á netinu (with -inu)? What case is that?

In Icelandic, “on the internet” is expressed with the definite form: netið (“the internet”).
The preposition á takes the dative for location (static position), so you get the dative definite: netinu.
Hence: á netinu = “online/on the internet.”
Contrast with motion: á netið = “onto the internet.”

Could I say á internetinu or something else?

Yes:

á netinu (most common)
á internetinu (also fine)
á vefnum (“on the web”) — a good stylistic alternative Avoid bare indefinite forms like á neti in this meaning.

Why is the subject omitted in the second clause: og fæ instead of og ég fæ?

Icelandic often drops a repeated subject after a coordinating conjunction. Both are correct:

Ég geri pöntun á netinu og fæ staðfestingu strax.
Ég geri pöntun á netinu og ég fæ staðfestingu strax. The first is smoother. After og, the finite verb can come first when the subject is omitted; this still respects Icelandic word-order patterns.

How do I conjugate gera (“to do/make”)?

Present: ég geri, þú gerir, hann/hún/það gerir, við gerum, þið gerið, þeir/þær/þau gera
Past: ég gerði, þú gerðir, hann/hún/það gerði, við gerðum, þið gerðuð, þeir/þær/þau gerðu
Supine/pp: gert (e.g., hef gert)

How do I conjugate fá (“to get/receive”), and why is it fæ here?

Present: ég fæ, þú færð, hann/hún/það fær, við fáum, þið fáið, þeir/þær/þau fá
Past: ég fékk, þú fékkst, hann/hún/það fékk, við fengum, þið fenguð, þeir/þær/þau fengu
Supine: fengið (e.g., hef fengið) It’s fæ because that’s the 1st person singular present form.

Why does staðfestingu end in -u? What case is it?

It’s the accusative singular of the feminine noun staðfesting (“confirmation”), used as the direct object of fæ.

Nom sg: staðfesting
Acc sg: staðfestingu
Dat sg: staðfestingu
Gen sg: staðfestingar (Plurals: nom/acc staðfestingar, dat staðfestingum, gen staðfestinga)

Where should I put strax?

Both are fine:

Ég fæ staðfestingu strax.
Ég fæ strax staðfestingu. End position is very common; putting strax early adds a bit of emphasis on immediacy. You can also front it for emphasis: Strax fæ ég staðfestingu, which is stylistic.

Do I need a comma before og here?

No. Icelandic generally doesn’t use a comma before og when joining two clauses with the same subject. Your sentence is punctuated correctly without a comma.

Why isn’t there a word for “a/an” before pöntun?

Icelandic has no indefinite article. Bare nouns serve that role. pöntun here means “an order.” If you need the definite (“the order”), you add a suffix: pöntunin (nom) or pöntunina (acc).

Is the present tense here habitual, and can it refer to the future?

Yes. Icelandic present is used for general truths/habits and, with context, for near-future plans. Alternatives:

Habit: Ég panta oft á netinu.
Ongoing: Ég er að panta á netinu (“I’m ordering online [right now]”).
Future intent: Ég ætla að panta á netinu (“I’m going to order online”).

Could I use another verb instead of gera pöntun?

Yes:

Ég panta á netinu… (most direct)
Ég legg inn pöntun á netinu… (very natural for “place an order”) All pair naturally with …og fæ staðfestingu strax.

Does pöntun ever mean “reservation/booking”?

Often, yes—especially with services: panta borð (book a table), pöntun for a reservation. You’ll also see bókun for bookings (e.g., travel). Context decides: for goods, pöntun is “order”; for services, it can be “reservation.”

Why not fái instead of fæ?

fái is the present subjunctive (used in subordinate clauses, wishes, hypotheticals). In a straightforward main-clause statement you use the indicative fæ. Example subjunctive: Svo að ég fái staðfestingu strax (“so that I get confirmation immediately”).