A blokk és a tartozék a táskában vannak.

Yes:

• A blokk = the blokk
• és = and
• a tartozék = the accessory / attachment
• a táskában = in the bag
• vannak = are

Grammatically, a blokk és a tartozék is the subject, a táskában is the location, and vannak is the verb are.

Because Hungarian often repeats the definite article when two separate definite nouns are joined by és.

So:

• a blokk és a tartozék = the block/receipt and the accessory

This sounds more natural than leaving the second article out. Repeating a makes it clear that both nouns are definite and separate items.

-ban / -ben is the suffix meaning in.

So:

• táska = bag
• táskában = in the bag

Hungarian usually expresses this kind of meaning with a suffix attached to the noun, instead of a separate word like English in.

Because the final a in táska changes to á before many suffixes.

So:

• táska
• táská-
• táskában

This is a very common pattern in Hungarian. Final a often becomes á, and final e often becomes é, when a suffix is added.

Because of vowel harmony.

Hungarian suffixes often come in two versions:

• -ban
• -ben

Words with mostly back vowels usually take -ban, and words with front vowels usually take -ben.

táska contains back vowels, so it takes -ban:

• táskában

Because the subject is plural in meaning.

Even though each noun is singular:

• a blokk = one item
• a tartozék = one item

together they form a compound subject:

• a blokk és a tartozék = two things

So Hungarian uses the plural form of to be:

• van = is
• vannak = are

Because the sentence is talking about one blokk and one tartozék, not several of each.

Hungarian, like English, can have:

• singular noun + singular noun
• but a plural verb because the two nouns together make a plural subject

So this is like English:

• The book and the pen are on the table.

You would not make book and pen plural there either.

That is a very good question.

In Hungarian, the present tense of to be is often omitted in the 3rd person singular in sentences like:

• A táska nagy. = The bag is big.

But with plural subjects, the form vannak is normally used:

• A táskák nagyok. = The bags are big.

Also, in location sentences like this one, van / vannak is normally present:

• A könyv az asztalon van. = The book is on the table.
• A könyvek az asztalon vannak. = The books are on the table.

So vannak is exactly what you expect here.

Hungarian word order is fairly flexible, but different orders change the emphasis.

This sentence:

• A blokk és a tartozék a táskában vannak.

is a natural way to say that the block/receipt and the accessory are the things being talked about, and the new information is where they are.

If you move a táskában earlier, you can put more emphasis on the location. So the order is not completely fixed, but the version given is a normal, neutral sentence.

Because és simply means and, and in a basic coordination of two nouns Hungarian normally does not use a comma before it.

So:

• a blokk és a tartozék

works just like:

• the block/receipt and the accessory

Yes, they matter a lot.

In Hungarian, accent marks are part of the spelling and show vowel length:

• a and á are different vowels
• e and é are different vowels

So you should treat them as real letters, not optional marks.

For example:

• táska
• táskában
• tartozék

should all be written with the correct accents.