אני מחפשת את הפותחן, כי אני רוצה לפתוח את הפחית.

Hebrew usually does not use a separate present-tense verb for to be.

So אני מחפשת literally looks more like I looking/searching, but in natural English it can mean I am looking for or I look for, depending on context.

That is very normal in Hebrew:

• אני מחפשת = I am looking for / I look for
• אני רוצה = I want

מחפשת is the feminine singular present-tense form.

Hebrew present-tense verbs agree with the subject in gender and number. Since the speaker is female, she says:

• אני מחפשת = a woman says I am looking for

A male speaker would say:

• אני מחפש

So even though אני means I for both men and women, the verb form shows the speaker’s gender.

Because in unpointed Hebrew spelling, some masculine and feminine forms look the same.

רוצה can be:

• rotze = masculine singular
• rotza = feminine singular

They are spelled the same: רוצה.

In this sentence, מחפשת already tells you the speaker is female, so אני רוצה is understood as feminine: I want said by a woman.

את is the marker of a definite direct object. It usually has no English translation.

So:

• את הפותחן = the opener as a direct object
• את הפחית = the can as a direct object

You use את when the direct object is definite, for example with ה- (the).

Compare:

• אני מחפשת פותחן = I’m looking for an opener
• אני מחפשת את הפותחן = I’m looking for the opener

Because the Hebrew verb לחפש works differently from English to look for.

In English, look for is a verb plus a preposition.
In Hebrew, לחפש is simply a transitive verb meaning to look for / to search for, and it takes a direct object.

So Hebrew says:

• אני מחפשת את הפותחן

Not something like I am looking for for the opener.

This is a very common thing in language learning: the Hebrew verb pattern does not always match the English one word-for-word.

The prefix ל- is part of the Hebrew infinitive, often corresponding to English to.

So:

• לפתוח = to open
• לחפש = to look for
• לרצות = to want

In this sentence:

• אני רוצה לפתוח = I want to open

So ל- here is doing the job of English to before a verb.

Yes. They come from the same Hebrew root: פ-ת-ח, which is connected with opening.

• לפתוח = to open
• פותחן = opener / opening tool

This is a very important feature of Hebrew: many words are built from the same root, so once you recognize the root, vocabulary becomes easier to connect.

The prefix ה- is the Hebrew definite article, meaning the.

So:

• פותחן = an opener / opener
• הפותחן = the opener
• פחית = a can
• הפחית = the can

Since both nouns are definite here, they also take את as direct objects:

• את הפותחן
• את הפחית

Hebrew often repeats the subject when starting a new clause, especially in everyday clear, natural speech.

So:

• אני מחפשת את הפותחן, כי אני רוצה לפתוח את הפחית

is completely normal.

In English, repeating I is also normal:

• I’m looking for the opener because I want to open the can.

In Hebrew, this repetition is especially useful because present-tense verb forms do not clearly show person the way past and future forms often do.

Here כי means because and introduces the reason:

• כי אני רוצה לפתוח את הפחית = because I want to open the can

So the sentence structure is:

• main clause + כי
  • reason clause

Also, in other contexts, כי can sometimes mean that, especially in more formal or literary Hebrew, but in this sentence it clearly means because.

Yes.

Hebrew present tense often covers both:

• a general present meaning: I look for
• an ongoing present meaning: I am looking for

Context tells you which one is meant. In this sentence, the natural meaning is I am looking for, because it sounds like something happening right now.