Meine Schwester holt das Maßband, damit wir die Wand genau messen können.

Because Schwester is a feminine noun.

The possessive word mein changes its ending to match the noun’s gender, number, and case. In the nominative singular feminine, it becomes meine.

So:

• mein Bruder = my brother
• meine Schwester = my sister

Here, meine Schwester is the subject of the sentence, so nominative is needed.

Holen usually means to fetch, to go and get, or to bring back after getting something.

So Meine Schwester holt das Maßband suggests that the sister is going to get the tape measure, probably from somewhere else, so it can be used.

This is a little different from:

• nehmen = to take
• bringen = to bring
• holen = to go get / fetch

So holt is a very natural choice here.

Because Maßband is a neuter noun, so it takes das in the nominative and accusative singular.

A useful thing to know about German compound nouns is that the last part usually determines the gender.
Here:

• das Band = the band / ribbon / tape
• so das Maßband is also neuter

That is why the sentence says das Maßband.

Because damit introduces a subordinate clause, and in German, subordinate clauses are separated by a comma.

So the sentence has:

• main clause: Meine Schwester holt das Maßband
• subordinate clause: damit wir die Wand genau messen können

That comma is not optional here; it is required in standard German punctuation.

Here, damit means so that or in order that. It introduces the purpose of the action in the main clause.

So the structure is:

• Meine Schwester holt das Maßband
• damit wir die Wand genau messen können

In other words: she gets the tape measure so that we can measure the wall accurately.

A very important learner point: damit is often used when the subject of the purpose clause is different from the subject of the main clause.

Here:

• main clause subject: meine Schwester
• subordinate clause subject: wir

That makes damit the natural choice.

Because um ... zu is usually used when the subject is the same in both parts of the sentence.

Compare:

• Ich hole das Maßband, um die Wand zu messen.
  = I get the tape measure in order to measure the wall.
  Same subject: I do both actions.

But in your sentence:

• Meine Schwester gets the tape measure
• wir measure the wall

Since the subjects are different, German normally uses damit:

• Meine Schwester holt das Maßband, damit wir die Wand genau messen können.

Because damit starts a subordinate clause, and in German subordinate clauses, the conjugated verb goes to the end.

Without a modal verb, you would expect something like:

• ..., damit wir die Wand genau messen.

But because there is a modal verb, the verb cluster goes to the end:

• messen können

And the finite/conjugated verb is können, so it comes last.

That is why the clause ends with:

• ... messen können

not

• ... können messen

This is because of the normal word order of a subordinate clause with a modal verb.

In a main clause, you would say:

• Wir können die Wand genau messen.

There, können is in second position.

But after damit, the clause becomes subordinate, so the verbs move to the end:

• ..., damit wir die Wand genau messen können.

So:

• main clause order: wir können messen
• subordinate clause order: wir messen können

That pattern is very common in German.

Because Wand is a feminine noun, and here it is the direct object of messen.

The verb messen takes the thing being measured as an accusative object:

• die Wand messen = to measure the wall

Since Wand is feminine, the accusative singular article is still die.

So:

• nominative: die Wand
• accusative: die Wand

That is why the form does not change here.

Genau is an adverb here, and it means accurately, exactly, or precisely.

It describes how we want to measure the wall:

• die Wand messen = measure the wall
• die Wand genau messen = measure the wall accurately / precisely

So it modifies the action messen, not the noun Wand.

Yes. Holt is grammatically present tense, but German often uses the present tense to talk about the near future when the context makes it clear.

So this sentence could mean something like:

• My sister is fetching the tape measure
• or My sister will fetch the tape measure

depending on the situation.

That is very normal in German. You do not always need a special future form.

Not with the same meaning and subject structure.

If you say:

• Meine Schwester holt das Maßband, um die Wand genau messen zu können,

the implied subject of messen zu können would normally still be meine Schwester.

That would suggest that she is the one measuring the wall.

But the original sentence says:

• damit wir die Wand genau messen können

which clearly means we are the ones who will be able to measure it.

So damit is better because it lets German state the different subject directly.

No, standard German normally requires the subject to be stated explicitly.

So in:

• damit wir die Wand genau messen können

you need wir because it tells us who can measure the wall.

Unlike some languages, German does not usually drop subject pronouns just because the verb ending already gives some information. So wir must stay.