Klucz jest głęboko w torbie.

Because the preposition w meaning in takes the locative case when it describes location.

• dictionary form: torba = bag
• after w for location: w torbie = in the bag

So:

• torba = the bag
• w torbie = in the bag

This is one of the most important case patterns in Polish:

• w domu = in the house
• w szkole = at school / in the school
• w torbie = in the bag

Klucz is in the nominative case because it is the subject of the sentence: the thing that is somewhere.

So the structure is:

• Klucz = subject
• jest = is
• głęboko w torbie = location / position

The basic dictionary form is also klucz, so here the nominative looks the same as the base form.

Because głęboko is an adverb, and here Polish uses an adverb to describe how far inside the bag the key is.

• głęboki = deep, as an adjective describing a noun
  • głęboka rzeka = a deep river
• głęboko = deeply / deep inside, as an adverb
  • głęboko w torbie = deep in the bag / deep inside the bag

So in this sentence, głęboko does not describe klucz directly. It describes the key’s position.

In a normal, complete sentence like this, jest is standard and expected.

• Klucz jest głęboko w torbie. = complete, neutral sentence

You may sometimes hear shortened speech like:

• Klucz głęboko w torbie.

But that sounds more like an informal fragment, note, or headline-style wording. For learners, the safe standard form is:

• Klucz jest głęboko w torbie.

Here w means in or inside.

So:

• w torbie = in the bag

A useful thing to know is that w can work with different cases depending on meaning:

• w + locative for location
  
  • w torbie = in the bag
• w + accusative for motion into something
  
  • wkładam klucz w torbę = I put the key into the bag

So in your sentence, because the key is already located there, Polish uses the locative: w torbie.

No, Polish word order is fairly flexible, but different orders change the focus or emphasis.

The most neutral version is:

• Klucz jest głęboko w torbie.

Other possible orders include:

• W torbie klucz jest głęboko.
• Głęboko w torbie jest klucz.

These are possible, but they sound more marked or literary, or they emphasize different parts of the sentence.

For everyday learning, the original order is the best one to use.

Yes. It means the key is deep inside the bag, not just somewhere in it.

Compare:

• Klucz jest w torbie. = The key is in the bag.
• Klucz jest głęboko w torbie. = The key is deep in the bag / deep inside the bag.

So głęboko adds the idea that the key may be hard to reach because it is far down inside.

A rough English-friendly guide is:

klooch yest gwem-BO-ko f TOR-bye

A few pronunciation notes:

• klucz sounds roughly like klooch
• jest sounds like yest
• gł in głęboko sounds like gw
• ę before b is pronounced roughly like em, so głę- sounds like gwem
• w torbie is pronounced more like f torbie in connected speech, because Polish w often sounds like f before a voiceless consonant

Stress in Polish usually falls on the second-to-last syllable:

• głęBOko
• TORbie

Normally, no. Here the correct form is w torbie.

Polish sometimes uses we instead of w to make pronunciation easier, especially before awkward consonant clusters, for example:

• we wtorek = on Tuesday
• we Wrocławiu = in Wrocław

But torbie does not need that extra vowel, so Polish says:

• w torbie

Klucz is masculine inanimate.

It matters in Polish because gender affects agreement in many places, especially in the past tense and with adjectives. In this present-tense sentence, you do not see much of that agreement, because jest is the same for all genders:

• klucz jest = the key is
• torba jest = the bag is
• dziecko jest = the child is

But if you added an adjective, gender would matter:

• mały klucz = a small key
• mała torba = a small bag

Yes. Depending on the exact meaning, Polish could also use:

• Klucz jest w torbie. = The key is in the bag.
• Klucz jest głęboko w środku torby. = The key is deep inside the bag.
• Klucz jest na dnie torby. = The key is at the bottom of the bag.

The original sentence is natural if you want to stress that the key is far inside the bag, not easy to get to.