Lijn de deuren uit en maak ze vast.

Because the full verb is uitlijnen, which is a separable verb in Dutch.

In a main clause or command, the first part stays with the conjugated verb, and the prefix moves to the end:

• uitlijnen → Lijn de deuren uit.

Compare:

• infinitive: de deuren uitlijnen
• command: Lijn de deuren uit
• subordinate clause: ... dat je de deuren uitlijnt

This is very common in Dutch.

Lijn is the imperative form: the form used for commands.

For most Dutch verbs, the informal imperative is just the stem:

• lijnen → stem lijn
• command: Lijn!

So:

• jij lijnt / hij lijnt = present tense
• Lijn ... uit! = command

An English speaker may expect something like a normal present-tense form, but Dutch usually uses the bare stem for commands.

It is a separable compound verb made of:

• uit
• lijnen

In this verb, uit is not being used very literally as out. It is just part of the fixed verb uitlijnen, which means to align something properly or bring it into line.

So it is better to learn uitlijnen as one vocabulary item, even though it splits in some sentence patterns.

Deuren is the plural of deur.

So:

• de deur = the door
• de deuren = the doors

Also, in Dutch, all plural nouns take the article de. So even if a singular noun might be het in some cases, the plural would still use de.

Ze means them and refers back to de deuren.

Dutch often avoids repeating the noun when it is already clear:

• Lijn de deuren uit en maak de deuren vast sounds repetitive.
• Lijn de deuren uit en maak ze vast sounds natural.

So this works just like English them.

In normal everyday Dutch, ze is the usual unstressed word for them.

That is why it appears here:

• maak ze vast

Hen is more formal and more strongly stressed. In ordinary instructions like this, ze is the natural choice.

So for a learner, the useful rule is:

• casual, common them = ze

Because the full verb is vastmaken, another separable verb.

Just like uitlijnen, it splits in a main clause or command:

• infinitive: vastmaken
• command: Maak ze vast
• subordinate clause: ... dat je ze vastmaakt

So both halves of the sentence use the same pattern:

• Lijn ... uit
• maak ... vast

Historically, yes, that is the idea, but in modern Dutch you should treat vastmaken as a normal verb meaning things like:

• fasten
• attach
• secure

So vast contributes the idea of being fixed or secure, but the whole expression is best learned as one verb.

Because this is a command.

Dutch imperatives usually leave out the subject, just like English:

• Align the doors
• Lijn de deuren uit

The sentence is understood as being addressed to the listener.

Each half follows this pattern:

• verb
• object
• separable particle

So:

• Lijn
  • de deuren
    • uit
• maak
  • ze
    • vast

This is an important Dutch pattern. English speakers often want to keep the verb together, but in main clauses Dutch commonly splits separable verbs this way.

Yes. In infinitives and many subordinate clauses, they usually stay together.

For example:

• Je moet de deuren uitlijnen en ze vastmaken.
• ... omdat je de deuren uitlijnt en ze vastmaakt.

So a useful contrast is:

• command/main clause: Lijn de deuren uit. Maak ze vast.
• infinitive/subordinate structure: uitlijnen, vastmaken

No. En is simply and.

It connects two commands:

• Lijn de deuren uit
• maak ze vast

So the sentence is really just two imperatives joined together.