Дверная петля скрипит, когда я открываю шкаф.

Дверная describes петля, not шкаф.

• петля is a feminine noun
• Russian adjectives must agree with the noun they modify in gender, number, and case
• so you get дверная петля, not дверной петля or дверное петля

Here, дверная is the feminine singular nominative form of the adjective.

Both patterns are possible in Russian, but they are used a little differently.

• дверная петля = a door hinge, the type or function of the object
• петля двери = the hinge of a specific door

The adjective pattern is very common in Russian for naming things by function or category. So дверная петля sounds natural as a standard term.

It is in the nominative case because it is the subject of the sentence: it is the thing that скрипит.

You can tell from the forms:

• дверная = feminine singular nominative adjective
• петля = feminine singular nominative noun

Шкаф is in the accusative case because it is the direct object of открываю.

But for many inanimate masculine singular nouns, the accusative looks exactly the same as the nominative. So:

• nominative: шкаф
• accusative: шкаф

That is why there is no visible change.

Compare with an animate masculine noun:

• я вижу брата not
• я вижу брат

Скрипит is the 3rd person singular present-tense form of скрипеть.

It matches the subject петля:

• я скриплю
• ты скрипишь
• он / она / оно скрипит
• они скрипят

So петля скрипит means the singular subject is doing the action.

This is about aspect.

• открываю is imperfective
• открою is perfective future
• открыть is the infinitive

In this sentence, открываю is used because the idea is something like whenever I open or when I am opening the cupboard. That is a repeated or general situation, so the imperfective is natural.

If you meant one single future event, Russian would usually use the perfective:

• Когда я открою шкаф, ...

So:

• когда я открываю шкаф = when / whenever I open the cupboard
• когда я открою шкаф = when I open the cupboard on a specific future occasion

Mostly when.

In this sentence, когда introduces a time clause: the squeaking happens at the time that I open the cupboard.

Depending on context, English might translate it as:

• when
• whenever
• sometimes even as or while

But the most straightforward understanding here is when.

Because когда я открываю шкаф is a subordinate clause.

In Russian, subordinate clauses are normally separated by a comma, whether they come first or second.

So both are correct:

• Дверная петля скрипит, когда я открываю шкаф.
• Когда я открываю шкаф, дверная петля скрипит.

Yes. Russian word order is more flexible than English word order.

For example, you can also say:

• Когда я открываю шкаф, дверная петля скрипит.

Both versions are correct. The difference is mostly in emphasis:

• Дверная петля скрипит, когда я открываю шкаф.
  starts with the main fact: the hinge squeaks
• Когда я открываю шкаф, дверная петля скрипит.
  starts with the time situation: when I open the cupboard

You can often leave it out in Russian, because the verb form already shows the person.

• открываю already means I open / I am opening

So this is also possible:

• Дверная петля скрипит, когда открываю шкаф.

Including я makes the subject more explicit. Omitting it can sound a bit more natural in some contexts, especially when the subject is already obvious.

Russian does not have words exactly like English a and the.

So дверная петля can mean:

• a door hinge
• the door hinge

Context tells you which one is meant. In this sentence, most people would understand it as a specific hinge in the situation being described.

If Russian wants to be more specific, it can use other tools, such as:

• эта дверная петля = this hinge
• word order
• general context

The standard stress is:

• дверна́я петля́ скрипи́т, когда́ я открыва́ю шкаф

A few helpful points:

• дверна́я — stress on -на́-
• петля́ — stress on the last syllable
• скрипи́т — stress on the last syllable
• когда́ — stress on the last syllable
• открыва́ю — stress on -ва́-

Stress matters in Russian, so it is worth learning words with the stress marked early on.