היא חותכת את תפוחי האדמה, ואני חותך את הבצל לארוחת הערב.

Because Hebrew present-tense verbs agree with the subject’s gender and number.

• היא חותכת = she is cutting / she cuts
• אני חותך = I am cutting / I cut said by a male speaker

If the speaker were female, it would be:

• אני חותכת

So in this sentence, היא is feminine, and אני is apparently a man.

את marks a definite direct object. It usually is not translated into English.

In this sentence:

• היא חותכת את תפוחי האדמה
• אני חותך את הבצל

Both תפוחי האדמה and הבצל are definite nouns, so Hebrew uses את before them.

A useful rule:

• If the direct object is definite, use את
• If it is indefinite, usually no את

For example:

• אני חותך בצל = I am cutting an onion / onion
• אני חותך את הבצל = I am cutting the onion

Hebrew commonly says potatoes as תפוחי אדמה, which literally means apples of the earth/ground.

This is a construct chain:

• תפוחי = apples of...
• האדמה = the ground / the earth

Together:

• תפוחי אדמה = potatoes
• תפוחי האדמה = the potatoes

So even though it looks like multiple words, it functions as one noun phrase meaning potatoes.

This is because of how definiteness works in a Hebrew construct chain.

In a construct chain, the whole phrase becomes definite if the second noun is definite.

So:

• תפוחי אדמה = potatoes
• תפוחי האדמה = the potatoes

You do not usually put ה on the first noun in this structure. The definiteness is shown on the second part: האדמה.

Because לארוחת הערב is not a direct object. It is a prepositional phrase.

• את תפוחי האדמה = the direct object
• את הבצל = the direct object
• לארוחת הערב = for dinner / for the evening meal

The word את is only used before definite direct objects, not before phrases introduced by prepositions like ל־ (to / for).

לארוחת הערב means for dinner or more literally for the evening meal.

It is made up of:

• ל־ = to / for
• ארוחת = meal of...
• הערב = the evening

So:

• ארוחת ערב = dinner / evening meal
• ארוחת הערב = the dinner / the evening meal
• לארוחת הערב = for the dinner / for dinner

Notice that ל + ה often combine in spelling:

• ל + ארוחת is just לארוחת
• there is no separate את here because this is a prepositional phrase

Yes. In modern Hebrew, what learners often call the present tense is historically based on participles, but functionally it is the normal way to say am cutting / cut in the present.

So:

• חותך = cutting / cuts
• חותכת = cutting / cuts

Depending on context, the sentence can mean:

• She is cutting the potatoes, and I am cutting the onion for dinner or
• She cuts the potatoes, and I cut the onion for dinner

Usually context tells you which English translation sounds best.

Often, yes.

Because the present-tense form shows gender and number, Hebrew can sometimes omit the subject pronoun when it is clear from context.

For example:

• חותכת את תפוחי האדמה, ואני חותך את הבצל
• or even
• חותכת את תפוחי האדמה, וחותך את הבצל

However, speakers often keep pronouns:

• for clarity
• for emphasis
• when contrasting subjects

In this sentence, היא ... ואני ... makes the contrast very clear: she is doing one thing, and I am doing another.

Because the Hebrew word for and, ו־, is normally attached directly to the following word as a prefix.

So:

• ו = and
• אני = I
• ואני = and I

This is extremely common in Hebrew. The conjunction ו־ is almost always written attached to the next word.

That is just the content of this particular sentence: one person is cutting the potatoes, and the other is cutting the onion.

Grammatically:

• תפוחי האדמה is plural
• הבצל is singular

This does not affect the form of חותך / חותכת, because the verb agrees with the subject (she, I), not with the object.

Not if you want the same meaning.

• לערב means for the evening / by evening
• לארוחת הערב means for dinner

So לארוחת הערב is the natural phrase here because the cutting is being done as preparation for the meal.

Only the first-person verb would need to change:

• היא חותכת את תפוחי האדמה, ואני חותכת את הבצל לארוחת הערב.

That is because אני does not itself show gender, but the present-tense verb does:

• male speaker: אני חותך
• female speaker: אני חותכת

A common pronunciation guide would be:

Hi khotékhet et tapukhéi ha-adamá, va-aní khotékh et ha-batsál le-arukhát ha-érev.

A few notes:

• ח is a throat sound, often written kh
• stress is usually near the end:
  • khotékhet
  • adamá
  • batsál
  • arukhát
  • érev

If you are learning to read naturally, it is better to use this only as support and keep practicing from the Hebrew script too.