Learn Hardcore Finnish: Minulla ei ollut vielä ajokorttia, joten en ollut ajanut itse tämän vilkkaan risteyksen läpi. - I didn’t have a driving licence yet, so I had not driven through this busy intersection myself.

Finnish usually expresses possession with the adessive case (minulla, on me) plus the verb olla (to be), not with a direct verb meaning to have.

Minulla on ajokortti = I have a driver’s license. (literally: On me is a driver’s license.)
In the past tense, this becomes: Minulla oli ajokortti = I had a driver’s license.
In the negative past: Minulla ei ollut ajokorttia = I didn’t have a driver’s license.

You cannot say En ollut ajokorttia, because olla here is not conjugated with minä as its subject in the normal way; the grammatical subject is the thing possessed (ajokortti), and the possessor is in adessive (minulla). In negative existential/possessive sentences, the verb is in the 3rd person singular with ei: ei ollut.

Why is ajokorttia in the partitive case and not ajokortti?

In negative possession with olla, the thing possessed typically appears in the partitive:

Minulla on ajokortti. – positive, nominative ajokortti
Minulla ei ole ajokorttia. – negative, partitive ajokorttia
In the past: Minulla ei ollut ajokorttia.

This is a standard pattern:

Minulla on auto. → Minulla ei ole autoa.
Hänellä oli rahaa. → Hänellä ei ollut rahaa.

So ajokorttia is the partitive singular of ajokortti, used because the sentence is negative and uses the Minulla on / Minulla ei ole type of possession.

What is the function of vielä in Minulla ei ollut vielä ajokorttia? Could it go in a different position?

Vielä means yet in this context and emphasizes that at that time the situation was still unfinished: you did not yet have the license.

Minulla ei ollut vielä ajokorttia. = I did not yet have a driver’s license.

Word order is quite flexible. You could say:

Minulla ei vielä ollut ajokorttia. – also common; some feel this stresses the time a bit more.
Minulla ei ollut ajokorttia vielä. – possible, a bit more conversational, with vielä sounding a bit like an afterthought.

All three are grammatically fine. The version given is very natural and neutral.

Why does the second clause use en ollut ajanut (past perfect) instead of just en ajanut (simple past)?

En ollut ajanut is the past perfect (pluperfect), formed with olla in the past + the active past participle:

ajaa → past participle ajanut
olin ajanut = I had driven
en ollut ajanut = I had not driven

The past perfect is used to talk about something that had (not) happened before another past moment. Here:

At that time, you didn’t yet have a license.
By that point, you had not (yet) driven through that intersection yourself.

So you have:

Simple past: Minulla ei ollut vielä ajokorttia (I did not yet have…)
Past perfect: en ollut ajanut (I had not driven… before that moment).

If you said joten en ajanut itse tämän vilkkaan risteyksen läpi, it would sound more like a single event in the past (so I didn’t drive through this busy intersection (that time)), rather than describing your experience up to that point. Both can be correct, but the nuance is different.

How is en ollut ajanut formed, exactly?

En ollut ajanut = I had not driven is:

en – 1st person singular of the negative verb
ollut – past tense of olla
ajanut – active past participle of ajaa

Pattern:

Minä olin ajanut. – I had driven.
Minä en ollut ajanut. – I had not driven.

Other persons follow the same model:

Olet ajanut. → et ole ajanut. – you have driven / have not driven
Oli ajanut. → ei ollut ajanut. – he/she had driven / had not driven

Why is there no minä in joten en ollut ajanut?

In Finnish, subject pronouns (minä, sinä, hän etc.) are often omitted if the person is clear from the verb ending and the context.

en ollut ajanut has the -n ending in en, marking 1st person singular.
The previous clause also clearly refers to me (Minulla ei ollut vielä ajokorttia).

So minä is understood and usually left out:

Joten en ollut ajanut itse… = So I hadn’t driven myself…

You could say joten minä en ollut ajanut, but that usually adds emphasis to minä (contrasting with someone else).

What does itse do here, and why is it placed after ajanut?

Itse adds emphasis roughly like myself in English:

en ollut ajanut itse = I had not driven myself.

It can highlight that:

you personally didn’t do the driving (someone else did), or
you didn’t do it by your own effort.

The position is somewhat flexible, but there is a nuance:

en ollut ajanut itse – most natural here; focus on the driving itself being done by me or not.
en ollut itse ajanut – can put a bit more emphasis on I myself (as opposed to some other person).

Both are grammatical; the original word order is very typical in this kind of sentence.

Why is it tämän vilkkaan risteyksen läpi and not something like tämä vilkas risteys läpi?

The postposition läpi (through) normally requires the preceding noun phrase to be in the genitive:

risteys (nominative) → risteyksen (genitive)
tämä → tämän
vilkas → vilkkaan

So you get the full phrase in the genitive:

tämän vilkkaan risteyksen läpi = through this busy intersection

The entire noun phrase (tämän vilkkaan risteyksen) is in the genitive because it is governed by läpi. You cannot leave it in nominative here.

Why does vilkas become vilkkaan in tämän vilkkaan risteyksen?

Vilkkaan is the genitive singular form of vilkas (busy). Two things are happening:

Case:
- The adjective must agree with the noun in case. Since risteys → risteyksen (genitive), vilkas must also go to genitive: vilkkaan.
Consonant gradation:
- The stem alternates between vilkas (weak grade) and vilkka- (strong grade).
- When forming the genitive, the strong grade appears: vilkka-
  - -n → vilkkaan.

So: tämä vilkas risteys (nominative) → tämän vilkkaan risteyksen (genitive).

Can the order tämän vilkkaan risteyksen läpi be changed to läpi tämän vilkkaan risteyksen?

Yes, you can say:

…en ollut ajanut itse tämän vilkkaan risteyksen läpi.
…en ollut ajanut itse läpi tämän vilkkaan risteyksen.

Both are grammatical. The first ([noun phrase] + läpi) is very common with läpi. The second (läpi + [noun phrase]) is also fine but may sound a tiny bit more emphatic on through as a path.

In everyday speech and writing, tämän vilkkaan risteyksen läpi is more typical.

Why is risteyksen (genitive) used instead of risteyksestä or risteyksessä?

Different cases answer different spatial questions:

risteys – intersection (basic form)
risteyksessä – in the intersection
risteyksestä – from the intersection
risteyksen läpi – through the intersection

The postposition läpi governs the genitive (risteyksen). If you used risteyksessä, you’d get something like in the intersection through, which does not match the standard pattern with läpi. For the meaning drive through X, the natural structure is:

ajaa X:n läpi → ajaa risteyksen läpi.

What does joten do here, and how is it different from koska?

Joten is a conjunction of result, roughly so, therefore:

Minulla ei ollut vielä ajokorttia, joten en ollut ajanut…
= I didn’t yet have a driver’s license, so I hadn’t driven…

Koska is a causal conjunction, because:

Koska minulla ei ollut vielä ajokorttia, en ollut ajanut itse tämän vilkkaan risteyksen läpi.
= Because I didn’t yet have a driver’s license, I hadn’t driven…

Meaning-wise, these two versions describe the same cause–effect relationship, but:

joten introduces the result clause (so...).
koska introduces the reason clause (because...).

How would this sentence look in the present tense instead of the past?

A present-tense version could be:

Minulla ei vielä ole ajokorttia, joten en ole ajanut itse tämän vilkkaan risteyksen läpi.
= I don’t yet have a driver’s license, so I haven’t driven through this busy intersection myself.

Changes:

ei ollut → ei ole (present of olla)
en ollut ajanut → en ole ajanut (present perfect: I have not driven).
The rest of the structure stays the same.