Wichtige Wörter unterstreiche ich im Text, damit ich sie später schneller finde.

German often puts the most important or most topical element first. Here, Wichtige Wörter is moved to the front for emphasis.

The more neutral order would be:

Ich unterstreiche wichtige Wörter im Text, damit ich sie später schneller finde.

Starting with Wichtige Wörter makes those words stand out more.

Because German main clauses follow the verb-second rule. The conjugated verb must be in the second position.

So if Wichtige Wörter takes the first position, the verb unterstreiche must come next, and the subject ich comes after it:

Wichtige Wörter | unterstreiche | ich ...

This is very common in German word order.

German can use a noun without an article when speaking in a general or indefinite way, especially in the plural.

So wichtige Wörter means important words in a general sense, not the important words.

Compare:

• wichtige Wörter = important words
• die wichtigen Wörter = the important words

Here the speaker means important words in general, so no article is needed.

Because the adjective is used before a plural noun without an article.

When there is no article, the adjective has to carry more grammatical information itself. That is why you get:

wichtige Wörter

This is a normal adjective ending for plural nouns in this kind of structure.

It is in the accusative plural, because it is the direct object of unterstreiche.

The person doing the action is ich.
The thing being underlined is wichtige Wörter.

Even though Wichtige Wörter comes first in the sentence, it is still the object, not the subject. German word order can move elements around, but their grammatical role stays the same.

No. unterstreichen meaning to underline is an inseparable verb.

That is why it stays together:

• ich unterstreiche
• du unterstreichst
• er unterstreicht

And in the perfect tense:

• ich habe unterstrichen

There is no extra ge- added.

im is a contraction of in dem.

So:

• im Text = in the text

Here it uses the dative because it refers to location, not movement. The idea is inside the text or within the text.

Here damit introduces a purpose clause. It means so that or in order that.

So:

..., damit ich sie später schneller finde.
= ..., so that I can find them more quickly later.

A clause with damit has its conjugated verb at the end, which is why finde comes last.

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

So the structure is:

main clause, subordinate clause

That is why the comma is required here.

sie refers back to Wörter.

Since Wörter is plural, the pronoun is also plural:

• die Wörter → sie

So ich sie später schneller finde means I find them more quickly later.

Because finde agrees with the subject ich, not with sie.

In this clause:

• ich = subject
• sie = object

So the verb must be first-person singular:

• ich finde

Even though sie is plural, it is not the subject.

Because später expresses time and schneller expresses manner, and German often puts time expressions before manner expressions.

So:

• später = later
• schneller = more quickly

Together:

sie später schneller finde
= find them more quickly later

Other orders can be possible for emphasis, but this order sounds natural.

Yes. Since the subject is the same in both parts of the sentence, German could also use um ... zu:

Wichtige Wörter unterstreiche ich im Text, um sie später schneller zu finden.

This is a little more compact.

A useful difference is:

• damit
  • full clause = can have a different subject
• um ... zu
  • infinitive = usually used when the subject stays the same

So both are possible here, but damit is also completely natural.