Learn Hardcore Finnish: Tämä on kirja, jota luen nyt. - This is the book that I am reading now.

joka – nominative (subject): Mies, joka lukee… (The man who reads…)
jonka – genitive: Mies, jonka kirjan luin… (The man whose book I read…)
jota – partitive: Kirja, jota luen… (The book that I’m reading…)
jossa – inessive: Talo, jossa asun… (The house in which I live…), etc.

So jota is simply joka in the partitive singular.

Why is jota used instead of joka here?

Because in the relative clause jota luen nyt, the pronoun is not the subject; it is the object of the verb luen (I read).

Finnish relative pronouns must be in the same case they would have if you wrote the noun directly:

Without a relative clause: Luen kirjaa nyt. (I’m reading a/the book now.) – kirjaa is in the partitive.
With a relative clause: Tämä on kirja, jota luen nyt. – jota takes the same case (partitive) that kirjaa would have.

If the pronoun were the subject, you’d use joka (nominative), but here it’s an object, so you need jota.

Which case is jota, and why is that case used?

Jota is the partitive singular form of joka.

It is partitive because:

It is the object of luen, and
The action is presented as ongoing / uncompleted (you are in the middle of reading the book).

Compare:

Luen kirjan. – I will read / I read the (whole) book. → kirjan (genitive, “total object”)
Luen kirjaa. – I am (in the process of) reading the book. → kirjaa (partitive, “partial / ongoing object)

Since the underlying object is kirjaa, the relative pronoun must match: jota (luen).

Why is there a comma before jota?

The comma separates the main clause from the relative clause:

Main clause: Tämä on kirja (This is a book.)
Relative clause: jota luen nyt (which I am reading now)

In Finnish, it’s common to put a comma before a non-restrictive relative clause (one that adds extra information rather than identifying which one among many). Here the idea is roughly:

This is a book, and I’m reading it now. (extra comment about the book)

So the comma marks jota luen nyt as additional information about kirja.

Could I leave out the comma (Tämä on kirja jota luen nyt)? Would the meaning change?

Grammatically, you can see both versions in real Finnish, but the comma slightly changes the feel:

With comma – Tämä on kirja, jota luen nyt.
→ more like extra information: This is a book; I happen to be reading it now.
Without comma – Tämä on kirja jota luen nyt.
→ more like a restrictive clause: This is the book that I’m reading now (as opposed to some other book).

In careful written Finnish, this restrictive–non‑restrictive distinction is usually reflected by the presence or absence of the comma, similar to English which, … vs that ….

Why is there no word for a/the before kirja?

Finnish does not have articles like a / an / the.

Definiteness and specificity are expressed by:

Context
Demonstratives like tämä (this), se (that), nämä, ne
Word order and emphasis

In Tämä on kirja, jota luen nyt, tämä already points to a specific object (“this”), so English could translate kirja as either a book or the book, depending on context. Finnish doesn’t mark that difference with a separate word.

Could I say Tämä on se kirja, jota luen nyt? How is that different?

Yes, Tämä on se kirja, jota luen nyt is perfectly correct and common.

Nuance:

Tämä on kirja, jota luen nyt.
→ Neutral: This is a book (which I’m reading now).
Tämä on se kirja, jota luen nyt.
→ Emphasises “that particular book” you have in mind or have mentioned before:
This is the (very) book that I’m reading now.

Using se adds a stronger sense of “the one we’re talking about”.

Where is the subject “I” in jota luen nyt? Why isn’t minä written?

The subject “I” is included in the verb ending -n in luen:

luen = I read / I am reading
luet = you (sg) read
lukee = he/she/it reads

Because the verb ending already shows the person and number, Finnish usually omits the personal pronoun unless you want to stress it:

Luen nyt. – I’m reading now. (normal)
Minä luen nyt. – I am the one who’s reading now. (emphasis on “I”)

So jota luen nyt naturally means which I am reading now without writing minä.

Can I move nyt somewhere else, like jota nyt luen?

Yes, you can. Typical options:

jota luen nyt – neutral, very common
jota nyt luen – puts slight emphasis on nyt (“right now”)

Both are grammatical. Usually, adverbs like nyt sit near the verb, and word order changes thematically what you emphasise, but the basic meaning stays the same.

Could I just say Luen nyt tätä kirjaa instead? Does it mean the same thing?

Luen nyt tätä kirjaa is also correct, but the focus is different:

Tämä on kirja, jota luen nyt.
→ Main point: identifying/describing the book (This is a book; I’m reading it now.)
Luen nyt tätä kirjaa.
→ Main point: what you are doing (I’m reading this book now.)

So they describe the same situation, but in a conversation you’d choose one or the other depending on whether you’re focusing on the book or on your activity.

How would the sentence change if the reading were finished (a completed action)?

If you want to present the reading as a completed whole, the object is no longer partitive but a total object (genitive), and the relative pronoun changes accordingly:

Ongoing: Tämä on kirja, jota luen nyt.
This is a book that I’m (currently) reading.
Completed: Tämä on kirja, jonka luin eilen.
This is the book that I read yesterday (finished it).

Here jonka is the genitive singular of joka, matching kirjan (luin kirjan = I read the book (completely)).