Mivel a karkötő hibátlan, kipróbálom, és az árus félreteszi.

Here mivel means since or because.

So:

Mivel a karkötő hibátlan = Since/Because the bracelet is flawless

A learner may know mivel as with what? / by what means?, and that is also a real Hungarian word. But in this sentence it is a conjunction introducing a reason clause.

Because Hungarian often omits the verb van (to be) in the present tense, third person when the predicate is a noun or adjective.

So:

• a karkötő hibátlan = the bracelet is flawless
• literally, Hungarian does not need a separate word for is here

But in other persons or tenses, the verb appears:

• Én hibátlan vagyok = I am flawless
• A karkötő hibátlan volt = The bracelet was flawless

Hungarian has two forms of the definite article:

• a before a consonant sound
• az before a vowel sound

So:

• a karkötő = the bracelet
• az árus = the vendor/seller

Both mean the. The choice is just based on pronunciation.

Kipróbálom can be broken down like this:

• ki- = a verbal prefix
• próbál = try
• -om = I with definite conjugation

So kipróbálom means roughly I try it out or, in this context, I try it on / I give it a try.

The important point is that Hungarian often packs a lot of information into one verb form.

Yes, Hungarian verbal prefixes can separate, but in a neutral declarative sentence they are usually attached.

So the neutral form is:

• kipróbálom

But separation happens in certain environments, especially with:

• negation: nem próbálom ki
• focus: most próbálom ki
• some future-like structures: ki fogom próbálni

So in this sentence, kipróbálom as one word is the normal neutral form.

Because the object is already understood from context: the bracelet.

Hungarian often drops an object if it is obvious. Also, the ending -om shows definite conjugation, which strongly suggests that the verb has a definite object.

So kipróbálom here really means:

• I try it
• with it = the bracelet

The same thing happens later with félreteszi: the seller puts it aside, where it is also understood.

Hungarian usually does not use subject pronouns unless they are needed for emphasis, contrast, or clarity.

The verb ending already tells you the subject:

• kipróbálom = I try it

So én is unnecessary unless you want emphasis:

• Én kipróbálom = I’ll try it / I’m the one who’ll try it

This is very common in Hungarian: the verb ending often carries the subject information.

Félreteszi comes from félretesz:

• félre- = aside / out of the way
• tesz = put
• teszi = he/she puts it in definite conjugation

So az árus félreteszi means:

• the seller puts it aside
• or more naturally, the seller sets it aside
• sometimes even the seller reserves it depending on context

Again, the object is not stated because it is understood to be the bracelet.

Formally, they are present tense forms.

However, Hungarian often uses the present tense for:

• immediate future
• planned next actions
• vivid narration

So depending on context, this can sound like:

• I try it on, and the seller puts it aside
• or I’ll try it on, and the seller will put it aside

Hungarian does have ways to make the future more explicit, for example with fog, but it is not always necessary.

Because hibátlan is an adjective, while hibátlanul is an adverb.

Here the sentence describes the bracelet itself:

• a karkötő hibátlan = the bracelet is flawless

That requires the adjective hibátlan.

By contrast:

• hibátlanul működik = it works flawlessly

There, hibátlanul modifies a verb, so the adverb is needed.

It has three parts:

1. Mivel a karkötő hibátlan
   = a reason clause: Since the bracelet is flawless

2. kipróbálom
   = main clause: I try it

3. és az árus félreteszi
   = coordinated clause: and the seller puts it aside

So the logic is:

reason -> my action -> seller’s action

This is a very natural Hungarian clause pattern.

Yes, and in many situations felpróbálom would be even more specific.

• felpróbálom = I try it on
  especially for clothes, jewelry, glasses, shoes, etc.

• kipróbálom = I try it out / test it

So with karkötő, both can work, but the nuance is a little different:

• felpróbálom a karkötőt focuses on putting it on to see how it looks or fits
• kipróbálom is broader and can sound more like I’ll give it a try

In real shop language, many speakers would naturally choose felpróbálom for a bracelet.