A garancialevél ugyan itt van, de a blokk nincs a táskában.

Here ugyan adds a concessive sense, something like admittedly, it is true that, or granted.

So A garancialevél ugyan itt van, de... has the feeling of:

• The warranty card is here, admittedly, but...
• The warranty card is here, true, but...

It often is not translated word for word in natural English, but it strengthens the contrast with de = but.

Yes. You can say:

A garancialevél itt van, de a blokk nincs a táskában.

That is still correct. Without ugyan, the sentence sounds more neutral. With ugyan, the contrast feels a bit stronger: yes, this part is true, but there is still a problem.

a / az is the Hungarian definite article, meaning the.

Hungarian uses:

• a before consonant sounds
• az before vowel sounds

So here:

• a garancialevél = the warranty card/document
• a blokk = the receipt
• a táskában = in the bag

It is a compound noun:

• garancia = guarantee / warranty
• levél = letter / document

So garancialevél literally means something like warranty document or guarantee letter. In real usage, it often corresponds to warranty card, warranty paper, or guarantee certificate.

Hungarian makes a lot of compound nouns like this.

-ban / -ben means in or inside.

• táska = bag
• táskában = in a bag / in the bag
• a táskában = in the bag

The form depends on vowel harmony:

• -ban
• -ben

Here the word takes -ban, so táskában.

In this kind of 3rd-person present-tense sentence, Hungarian uses nincs as the negative form of van.

So:

• itt van = is here
• nincs a táskában = is not in the bag

nem van is not standard Hungarian here.

Hungarian often leaves out is in simple descriptive sentences in the present tense:

• A táska nagy. = The bag is big.

But when talking about location or existence, Hungarian normally uses van / nincs:

• A garancialevél itt van. = The warranty card is here.
• A blokk nincs a táskában. = The receipt is not in the bag.

So this sentence needs van / nincs because it is about where something is.

Itt van is the normal, neutral order for is here.

In Hungarian, place expressions often come before van:

• itt van = is here
• ott van = is there
• a táskában van = is in the bag

van itt is possible, but it usually sounds marked or gives a different emphasis.

In everyday Hungarian, blokk commonly means a shop receipt, especially in spoken language.

Depending on context, you may also see:

• nyugta = receipt
• számla = invoice / bill, sometimes a more formal receipt

But blokk is very common for the small paper receipt you get in a store.

Because de means but, and in Hungarian it normally introduces a new clause here.

So the sentence has two parts:

• A garancialevél ugyan itt van
• de a blokk nincs a táskában

The comma helps separate the two contrasting clauses.

Yes, but the emphasis changes.

• A blokk nincs a táskában.
  This simply says: The receipt is not in the bag.

• A blokk nem a táskában van.
  This puts stronger focus on the bag as the location, with a sense like: The receipt is not in the bag; it is somewhere else.

So both are possible, but they are not identical in emphasis.