Draai de schroef steviger vast, zodat de plank goed hangt.

Yes. The verb here is the separable verb vastdraaien, which means to tighten, to screw tight, or more literally to turn fixed.

In Dutch main clauses, separable verbs split:

• Ik draai de schroef vast.
• Draai de schroef vast.

So:

• draai = the conjugated verb
• vast = the separable particle, placed later in the sentence

If you used the infinitive, it would stay together:

• Je moet de schroef vastdraaien.

And in a subordinate clause, it also stays together:

• ..., omdat hij de schroef vastdraait.

Steviger is the comparative form of stevig.

Basic meanings:

• stevig = firm, solid, sturdy
• steviger = firmer, more securely, more firmly

In this sentence, steviger works like an adverb in English: more firmly.

So:

• Draai de schroef vast = Tighten the screw.
• Draai de schroef steviger vast = Tighten the screw more firmly / make it tighter.

Dutch often uses the same form for adjectives and adverbs, so steviger can mean firmer or more firmly, depending on context.

Because the sentence is asking for a change: the screw should be tightened more than it is now.

• stevig vastdraaien = tighten firmly
• steviger vastdraaien = tighten more firmly

So the comparative -er is important. It suggests that the current state is not firm enough, and you should increase it.

Because this is the imperative, the command form.

In Dutch, commands usually leave out the subject:

• Draai de schroef vast. = Tighten the screw.

The understood subject is you.

You can add a subject sometimes for emphasis or politeness, but it is not necessary:

• Draai jij de schroef vast.
• Draait u de schroef vast.

In normal instructions, the short form without a subject is the most natural.

Because zodat introduces a subordinate clause.

In Dutch subordinate clauses, the conjugated verb usually goes to the end:

• ..., zodat de plank goed hangt.

Compare:

• Main clause: De plank hangt goed.
• Subordinate clause: ..., zodat de plank goed hangt.

So this is normal Dutch word order after words like:

• omdat = because
• zodat = so that
• als = if/when
• terwijl = while

Here zodat means so that.

It introduces the purpose or result of tightening the screw:

• Draai de schroef steviger vast, zodat de plank goed hangt.
• Tighten the screw more firmly, so that the plank hangs properly.

So the second part explains why you should do the first part.

Yes. In Dutch, hangen is used for things that are suspended, attached to a wall, or positioned vertically in a hanging way.

So if a plank is mounted and supported on a wall, Dutch can naturally use hangen.

This is broader than English hang in some contexts. Dutch often uses:

• staan for things standing upright
• liggen for things lying flat
• hangen for things hanging or mounted

So de plank hangt goed means the plank is hanging/mounted properly and securely.

Here goed means properly, correctly, or securely, not just well in a vague sense.

So de plank goed hangt suggests:

• it is straight enough
• it is attached properly
• it is secure
• it is not loose or crooked

Dutch often uses goed this way, where English might prefer properly.

Yes, those are possible in some contexts, but the nuance changes a little.

• vaster = more tightly / more fixed
• strakker = tighter, tenser
• steviger = more firmly / more solidly

In this sentence, steviger sounds natural because the goal is a firm, secure result.
vaster is also possible and may sound even more directly connected to fastening:

• Draai de schroef vaster.

But steviger vastdraaien emphasizes solidity and security.

Because both schroef and plank are common-gender nouns in Dutch, and common-gender singular nouns take de.

So:

• de schroef = the screw
• de plank = the plank

Unfortunately, for many nouns you simply have to learn whether they take de or het.

A useful detail:

• Diminutives are always het
• het schroefje = the little screw
• het plankje = the little plank

Because steviger modifies the action, and the separable particle vast normally stays in its usual final position in the main clause.

So Dutch naturally says:

• Draai de schroef steviger vast.

Not:

• Draai de schroef vast steviger.

You can think of steviger as describing how you do the fastening, while vast remains the particle belonging to vastdraaien.