Learn Hardcore Dutch: Mijn eerste poging is mislukt, maar ik blijf oefenen. - My first attempt has failed, but I keep practicing.

Eerste is an ordinal adjective (first, second, third, …) that goes in front of a noun: mijn eerste poging, de eerste dag, zijn eerste auto.
Eerst is usually an adverb meaning first / first of all / before anything else: Ik ga eerst eten, Eerst lees ik de tekst.
So you use eerste before a noun, and eerst mostly on its own in the sentence.

What exactly is poging, and what article does it take?

Poging means attempt/try and it uses the article de: de poging (singular), de pogingen (plural).
Typical collocation: een poging doen (om … te …) = to make an attempt (to …).
So you could also say: Ik deed een poging, maar die is mislukt.

Why is it mijn eerste poging, not eerste mijn poging or mijn poging eerste?

In Dutch, the normal order is:

Possessive: mijn / jouw / zijn / haar / ons / jullie / hun
Then ordinal or other adjectives: eerste, laatste, grote, nieuwe
Then the noun

So: mijn eerste poging, mijn nieuwe auto, zijn laatste kans.
The other orders (eerste mijn poging, mijn poging eerste) are ungrammatical in standard Dutch.

Why is it is mislukt and not heeft mislukt?

The verb mislukken (to fail, not succeed) is an intransitive verb that takes zijn as its auxiliary in the perfect tense:

De poging is mislukt.
Het experiment is mislukt.

You use hebben with most transitive verbs (that take a direct object):

Ik heb het examen gehaald.
But with verbs like komen, gaan, slagen, gebeuren, mislukken, you generally use zijn.

What part of speech is mislukt here, and can it also be an adjective?

In mijn eerste poging is mislukt, mislukt is the past participle of mislukken used in a perfect tense construction with zijn.
It can also be used as an adjective meaning failed / botched:

Een mislukte poging (a failed attempt)
Een mislukte taart (a failed cake / a cake that went wrong)

What is the nuance difference between mislukt and niet gelukt?

Both can express failure, but there’s a nuance:

mislukt often sounds a bit stronger or more negative, sometimes with a sense of going wrong:
De poging is mislukt. = The attempt failed / went wrong.
niet gelukt is more neutral:
De poging is niet gelukt. = The attempt did not succeed.

In many contexts they are interchangeable, but mislukt can feel slightly harsher or more definite.

What does maar do in this sentence, and is the comma before it required?

Maar is a coordinating conjunction meaning but, linking two main clauses:
Mijn eerste poging is mislukt, maar ik blijf oefenen.

A comma before maar is standard and recommended in writing, because you are joining two independent clauses.
In informal writing, some people may skip it, but with the comma is the norm.

How does blijven + infinitive work in ik blijf oefenen?

Blijven + infinitive means to keep doing / to continue doing something.
Structure: subject + blijven (conjugated) + infinitive at the end.

Examples:

Ik blijf oefenen. – I keep practicing.
We blijven proberen. – We keep trying.
Hij blijft lachen. – He keeps laughing.

So ik blijf oefenen literally means I stay practicing, but functionally I keep practicing.

Why is the verb order ik blijf oefenen and not ik oefenen blijf?

In a main clause, Dutch word order is:

Conjugated (finite) verb in second position: blijf
Other verbs (infinitives, participles) go to the end: oefenen

So: Ik blijf oefenen. = subject (ik) + finite verb (blijf) + infinitive (oefenen).
Ik oefenen blijf would be incorrect word order for a normal main clause.

How would this sentence change in other tenses, like past or future?

Some common variants:

Simple past:
Mijn eerste poging mislukte, maar ik bleef oefenen.
(My first attempt failed, but I kept practicing.)
Future:
Mijn eerste poging zal mislukken, maar ik zal blijven oefenen.
(My first attempt will fail, but I will keep practicing.)
Present perfect for the second clause:
Mijn eerste poging is mislukt, maar ik ben blijven oefenen.
(My first attempt failed, but I kept on practicing.)
Here, blijven uses zijn in the perfect: ik ben blijven oefenen.