Ég þakka fyrir góða þjónustu þegar ég fæ reikninginn.

Because the verb að þakka (to thank) is conjugated for 1st person singular in the present tense:

• ég þakka = I thank
• þú þakkar = you (sg) thank
• hann/hún/það þakkar = he/she/it thanks
• við þökkum = we thank
  So Ég þakka is the correct match for ég.

Að þakka typically takes:

• a direct object in the accusative (the person/thing you thank), and/or
• the fixed prepositional phrase þakka fyrir + accusative to express what you’re thanking for.

Here, fyrir governs the accusative, so:

• góða is accusative singular masculine (agreeing with þjónustu as used here)
• þjónustu is in the accusative (from þjónusta)

So þakka fyrir góða þjónustu = “thank for good service.”

Góða is the adjective góður (“good”) inflected to agree with the noun phrase þjónustu in case, number, and gender. In this sentence it appears as accusative singular, and the adjective takes the corresponding form góða.

(Adjective endings are one of the big “moving parts” in Icelandic—seeing -a often signals an oblique case form like accusative/dative/genitive, depending on the noun phrase.)

It’s indefinite: góða þjónustu = “good service” (in general), not “the good service.” Icelandic typically marks definiteness either by:

• the suffixed definite article on the noun (e.g., þjónustan = “the service”), or
• sometimes hin in more formal/contrastive styles.

Since the sentence is thanking for good service as a general description, the indefinite form is natural.

Both can occur, but they emphasize slightly different things:

• Ég þakka þér = “I thank you” (thanking a person; object is the person)
• Ég þakka fyrir þjónustuna = “I thank you for the service” (thanking for something)

Using fyrir cleanly introduces what you’re grateful for.

Þegar can mean “when,” and depending on context it can also imply a habitual sense like “whenever.” In a sentence about a repeated situation (like paying at a restaurant), þegar often feels like “when/whenever I get the bill.”

If you want to force the “every time” meaning more explicitly, you might add something like alltaf (“always”), but it isn’t required.

Because að fá (“to get/receive”) is an irregular verb. Present tense:

• ég fæ
• þú færð
• hann/hún/það fær So ég fæ is the correct 1st person singular form.

• reikningur = “a bill/account” (nominative singular, indefinite)
• reikninginn = “the bill” (accusative singular, definite)

Here, reikninginn is definite (“the bill”) and it’s in the accusative because it’s the direct object of fæ (“get/receive”).

Yes, that’s a very normal alternative. Icelandic is flexible with adverbial clauses. Two common patterns are:

1) Main clause first:
Ég þakka ... þegar ég fæ ...

2) Subordinate clause first (often with a comma in writing):
Þegar ég fæ ..., þakka ég ...

Both are correct; the second often feels slightly more “narrative” or formal.

Yes. Icelandic subordinate clauses typically keep the subject before the verb in a straightforward way, as here:
þegar [ég] [fæ] [reikninginn]

You don’t usually invert to fæ ég after þegar (that inversion is more typical in main clause questions or when something is moved to the front of a main clause).

A rough guide (exact pronunciation varies by speaker):

• Ég: sounds like “yeh(g)” with a short vowel; the g is often very soft or disappears in fast speech.
• þakka: þ is like English th in think; kk is a strong/long k sound.
• þjónustu: starts with th (as above); jó is like “yo”; u is rounded (not like English “oo” exactly).
• þegar: þ = “th”; first vowel like “theh”; the g can be soft.
• reikninginn: ei like “ay” (approximately); stress on the first syllable REIK-; -inn is the definite ending.

If you want, I can give IPA for each word too.