Learn Hardcore Hungarian: Ma nem megyek abba a boltba a sarkon. - Today I am not going to that shop on the corner.

So you cannot say *abba boltba (missing the article) in standard Hungarian.
You can say a boltba (without demonstrative) if you mean simply to the shop rather than to that shop.

Why is the verb megyek (present tense) used when the English translation is “I’m not going to that shop today” (future meaning)?

Hungarian very often uses the simple present to talk about the near future, especially with a time expression like ma (today), holnap (tomorrow), or este (in the evening).

Ma nem megyek abba a boltba.
= Today I’m not going to that shop. (future from an English point of view)
Holnap találkozom vele.
= I’ll meet him/her tomorrow.

If you really want to stress the future, you can use fog + infinitive:

Ma nem fogok abba a boltba menni.

But in everyday speech, Ma nem megyek abba a boltba is perfectly natural and usually preferred.

Why is the negative word nem placed right before megyek? Could it go somewhere else?

In neutral sentences, nem normally comes directly before the finite verb:

Ma nem megyek abba a boltba.
Nem látom őt.

If there is a verb prefix (like el-, be-, ki-), it interacts with nem and can move, but here megyek has no prefix, so nem just goes before it.

Other placements change the focus:

Ma abba a boltba nem megyek.
Focus on abba a boltba: It’s that shop that I’m not going to (maybe I’ll go to another shop).
Nem ma megyek abba a boltba.
Focus on ma: It’s not today that I’m going to that shop (but another day).

So in your sentence, Ma nem megyek... is the neutral, most common word order.

What is the exact role of -ba in boltba? How is it different from boltban?

The suffix -ba / -be is the illative case: it expresses movement into something.

bolt = shop
boltba = into the shop / to the shop (as destination)

-ban / -ben is the inessive case: it expresses location inside something (no movement).

boltban = in the shop

Compare:

Ma nem megyek abba a boltba.
= I’m not going into that shop (I won’t go there).
Ma nem vagyok abban a boltban.
= I’m not in that shop today.

So -ba = “into, to (as a goal)” and -ban = “in, inside (as a place where something is).”

Why is it boltba and not boltbe?

Hungarian uses vowel harmony:

After back vowels (a, á, o, ó, u, ú), you choose the back variant of a suffix.
After front vowels (e, é, i, í, ö, ő, ü, ű), you choose the front variant.

bolt has o, a back vowel → you use -ba:

bolt + -ba → boltba

With a front-vowel word, you would use -be:

kert + -be → kertbe (into the garden)
szék + -re → székre (onto the chair) – same principle with other suffixes

So boltbe would break vowel harmony and is incorrect.

Could I drop abba and just say Ma nem megyek a boltba a sarkon?

Yes, you can say:

Ma nem megyek a sarkon lévő boltba.
Ma nem megyek a boltba a sarkon. (colloquial but heard)

Without abba, you lose the explicit demonstrative “that”. The meaning becomes more like:

I’m not going to the shop on the corner (today).

With abba a boltba, you are clearly pointing to a specific, already-known shop:

I’m not going to that particular shop on the corner (the one we both know about).

So grammatically you can drop abba, but you slightly change the nuance (less “that one there,” more just “the shop on the corner”).
The original abba a boltba is the standard way to express that shop.

What does a sarkon mean exactly, and why is the ending -on used?

sarok = corner
sarkon = on the corner / at the corner

The suffix -on / -en / -ön is the superessive case, which generally means on (a surface), and sometimes at in English:

asztal (table) → asztalon (on the table)
téren (on the square / at the square)

With sarok, a sarkon usually means at the street corner, not literally on top of the corner. English often translates this as on the corner or at the corner.

Other options:

a saroknál = at/by the corner (using the postposition -nál/-nél)
a sarokhoz = (up) to the corner (goal of movement)

In your sentence, a sarkon tells us which shop: the shop on the corner.

Does a sarkon belong to megyek or to boltba? Is it “go on the corner” or “the shop on the corner”?

Semantically, a sarkon modifies boltba: it specifies which shop.

The structure is effectively:

abba a boltba [a sarkon]
= to that shop [which is] on the corner

There’s an understood relative structure like:

abba a boltba, amely a sarkon van
= to that shop that is on the corner

So it does not mean I go on the corner. It means I go to that shop which is on the corner (and here, specifically: I’m not going there).

Why isn’t there a personal pronoun like én (“I”) in the sentence?

Hungarian is a pro-drop language: subject pronouns are usually omitted when the verb ending already shows the person and number.

megyek = I go / I am going (1st person singular)
mész = you go (2nd person singular)
megy = he/she/it goes (3rd person singular)

So:

Ma nem megyek abba a boltba.
already clearly means I’m not going to that shop today.

You would add én only for emphasis or contrast:

Én ma nem megyek abba a boltba (de te mehetsz).
I’m not going to that shop today (but you can).

Why is it megyek and not some “definite” form like *megyem, since we have a specific shop?

The verb menni (to go) is intransitive in Hungarian: it does not take a direct object in the accusative case. Instead, it takes a destination in a case like -ba/-be, -hoz/-hez/-höz, etc.

Definite vs indefinite conjugation in Hungarian depends on the direct object, not on how specific the destination is.

Verb with direct object:
- Látok egy boltot. (I see a shop.) → látok (indefinite)
- Látom a boltot. (I see the shop.) → látom (definite)
Verb without direct object (like menni):
- Megyek a boltba. (I go to the shop.)
- There is no definite form *megyem here, because boltba is not a direct object; it’s a place expression.

So megyek is the only normal 1st person singular form for menni in this use.

Can I change the word order, for example: Abba a boltba ma nem megyek a sarkon? What changes?

Hungarian word order is flexible, but it changes focus. Some possibilities:

Ma nem megyek abba a boltba a sarkon.
Neutral: focus is mostly on the fact that today I’m not going to that (corner) shop.
Abba a boltba ma nem megyek (a sarkon).
Strong focus on abba a boltba:
It’s (specifically) that shop I’m not going to today (maybe I’ll go elsewhere).
Ma abba a boltba nem megyek a sarkon.
Focus is also on abba a boltba; “today, that shop is the one I’m not going to.”

In speech, intonation also plays a big role. Grammatically, several orders are possible, but the immediately pre-verbal position (just before nem / the verb) is the strong focus position. The given sentence is relatively neutral, with ma as a time frame and nem megyek as the main predicate.

Is there any difference between abba a boltba a sarkon and a more explicit form like abba a sarkon lévő boltba?

Both refer to that shop on the corner, but there is a stylistic difference.

abba a boltba a sarkon
Colloquial, “compressed”:
Literally “into that shop, on the corner” – the a sarkon acts like an afterthought or apposition describing the shop.
abba a sarkon lévő boltba
More explicit and a bit more formal or written:
Literally “into that shop which is located on the corner.”

Meaning-wise they are almost identical. The second version just spells out the relationship with lévő (“being / located”), while the original sentence leaves it implicit, relying on context and common patterns.