Kun jij mij de schroevendraaier aangeven?

Because this is a yes/no question. In Dutch, yes/no questions usually put the finite verb first.

• Statement: Jij kunt mij de schroevendraaier aangeven.
• Question: Kun jij mij de schroevendraaier aangeven?

So the word order changes in the same way English changes You can... to Can you....

Because the sentence is inverted: the verb comes before the subject in a question.

With jij, you often get:

• normal order: jij kunt
• question order: kun jij

So the -t disappears when jij comes after the verb.

You may also hear kan jij in everyday Dutch, but kun jij is a very standard form here.

Here, aangeven means to hand or to pass something to someone.

So in this sentence, it means something like:

• Could you pass me the screwdriver?

This verb has several meanings in Dutch depending on context. In other situations, aangeven can also mean:

• to indicate
• to point out
• to report

But with an object like de schroevendraaier, it clearly means hand/pass.

Because aangeven is a separable verb.

Its full dictionary form is aangeven, but in a main clause with a finite verb, it splits:

• Ik geef het aan.
• Kun jij mij de schroevendraaier aangeven?

In this sentence:

• kun = the finite verb part
• aan = the separated particle at the end
• geven is built into the infinitive aangeven

A helpful thing to remember is that many Dutch verbs with prefixes like aan-, op-, uit-, mee- are separable.

Because mij is the indirect object and de schroevendraaier is the direct object.

Dutch commonly puts:

1. the person receiving something first
2. the thing being passed second

So:

• mij = to me
• de schroevendraaier = the screwdriver

This order is especially common when the indirect object is a pronoun.

So Kun jij mij de schroevendraaier aangeven? sounds very natural.

Yes. In everyday Dutch, me is very common here:

• Kun jij me de schroevendraaier aangeven?

Very roughly:

• me = weaker, unstressed form
• mij = stronger, more emphatic form

In normal conversation, me often sounds more natural unless you want extra emphasis on me.

Because schroevendraaier is a de-word in Dutch.

Dutch nouns have to be learned with their article:

• de schroevendraaier
• not het schroevendraaier

Unfortunately, this usually has to be memorized word by word. There is not always a simple rule you can guess from.

It is a compound word:

• schroef = screw
• draaier = turner / thing that turns

So schroevendraaier is literally something like screw-turner, which matches the English idea of screwdriver.

Dutch makes compound nouns very freely, so long words like this are completely normal.

Yes. jij is informal, used with friends, family, coworkers you know well, children, and so on.

A more formal version is:

• Kunt u mij de schroevendraaier aangeven?

Here:

• u = formal you
• kunt matches u

If you want to sound even softer or more polite, you could say:

• Zou u mij de schroevendraaier kunnen aangeven?

That is closer to Could you pass me the screwdriver?

Dutch can leave it out, yes. The sentence is already a polite request because of kun jij... ?

You can add please, but Dutch often softens requests in other ways, especially with even:

• Kun jij mij even de schroevendraaier aangeven?
• Kun jij mij de schroevendraaier aangeven, alsjeblieft?

Very often, even makes the request sound natural and friendly, even though it literally means for a moment.

A very natural everyday version would be:

• Kun je me even de schroevendraaier aangeven?

Compared with the original:

• jij often becomes je
• mij often becomes me
• even is often added to make the request sound smoother

So the original sentence is correct, but the version above may sound a bit more conversational.