Sie markiert Schrauben, damit sie das Gerät zusammenbauen kann.

At the start of a German sentence, the first word is capitalized no matter what it is, so Sie here is not enough by itself to tell you the pronoun meaning.

It could theoretically be:

• she
• they
• formal you

The second pronoun is sie with a lowercase s, so that one can only mean she or they, not formal you.

So the sentence form alone is somewhat ambiguous, and context tells you which meaning is intended. If your lesson gives the meaning as singular, then read it as she.

This is a basic German word-order pattern:

• In a main clause, the finite verb usually comes in second position:
  Sie markiert Schrauben.

• After damit, you have a subordinate clause, and in subordinate clauses the finite verb goes to the end:
  damit sie das Gerät zusammenbauen kann

So the sentence combines:

• main clause: Sie markiert Schrauben
• subordinate purpose clause: damit sie das Gerät zusammenbauen kann

That is why the verb placement changes.

German often omits an article with plural nouns when they are meant in a general or nonspecific way.

So:

• Schrauben = screws in general / some screws
• die Schrauben = the screws, a specific set already known in the context

Here, Schrauben without an article sounds natural if she is marking screws, but not a specifically identified set that has already been singled out.

Both are accusative, because both are direct objects:

• Schrauben is the thing she marks.
• das Gerät is the thing she assembles.

A useful detail:

• Schrauben is plural, and without an article its form does not visibly change here.
• das Gerät is neuter singular, and the article das is the same in both nominative and accusative.

So even though both are accusative, you do not see a dramatic form change in this sentence.

Damit introduces a purpose clause. It means something like so that or in order that.

So the structure is:

• action 1: She marks screws
• purpose: so that she can assemble the device

German uses damit when one action is done for the purpose of another action.

It is not the same as:

• weil = because
• dass = that

Yes, it could, because the subject is the same person in both parts.

A possible version is:

Sie markiert Schrauben, um das Gerät zusammenbauen zu können.

Why is that possible?

• um ... zu is commonly used when the subject of both actions is the same.
• damit is often used when you want to state the subject explicitly, or when the subjects are different.

So both are possible here, but they are built differently:

• damit sie das Gerät zusammenbauen kann
• um das Gerät zusammenbauen zu können

Zusammenbauen is a separable verb.

In a simple main clause, it usually splits:

• Sie baut das Gerät zusammen.

But it stays together:

• in the infinitive
• with a modal verb
• in many subordinate-clause verb clusters

So here:

• zusammenbauen stays together because it is an infinitive used with kann

That is why you get:

• ... das Gerät zusammenbauen kann

and not something split like ... baut ... zusammen.

Kann adds the idea of ability or possibility.

So the sentence is not just saying that she marks the screws so that she assembles the device. It is saying she marks them so that she can assemble it.

That makes the purpose a little more precise:

• the marking helps make the assembly possible
• it gives her the ability or practical means to do it

Without kann, the meaning would shift slightly toward the result itself rather than her ability to achieve it.

In this sentence, that is the most natural reading, but grammatically sie could still mean she or they. German pronouns often rely on context.

Here, though, the intended reading is clearly:

• She marks screws so that she can assemble the device.

That is also why damit works well here: it keeps the second clause explicit and easy to understand.