יש בחנות גם זיתים טובים וגם טחינה טרייה, אז אקנה את שניהם.

יש is the Hebrew way to say there is / there are in the present.

So:

• יש בחנות... = There is/are in the store...

Even though the sentence mentions more than one thing, Hebrew still uses יש. In the present tense, יש does not change for singular vs. plural.

Because it is made from:

• ב־ = in
• החנות = the store

When ב־ combines with ה־, they usually merge into one written word:

• ב + החנות → בחנות

So בחנות means in the store.

גם ... וגם means both ... and ... or sometimes also ... and also ....

In this sentence:

• גם זיתים טובים וגם טחינה טרייה
• both good olives and fresh tahini

It is a very common structure in Hebrew for linking two items.

In Hebrew, adjectives normally come after the noun, unlike in English.

So:

• זיתים טובים = olives good = good olives
• טחינה טרייה = tahini fresh = fresh tahini

This is the normal Hebrew word order for noun + adjective.

Because Hebrew adjectives must agree with the noun in gender and number.

• זיתים is masculine plural, so the adjective is טובים = masculine plural
• טחינה is feminine singular, so the adjective is טרייה = feminine singular

This kind of agreement is one of the most important things to notice in Hebrew.

Hebrew often leaves out subject pronouns when the verb already makes the subject clear.

• אקנה means I will buy
• The א־ at the beginning marks first person singular future

So אני אקנה is possible, but usually unnecessary unless you want emphasis.

אקנה is the future tense, first person singular, of לקנות (to buy).

So:

• אקנה = I will buy

In this sentence, after אז (so), it means:

• so I’ll buy...

Here אז means so.

So the sentence is structured like:

• there are both X and Y in the store,
• so I’ll buy both.

Depending on context, אז can also mean then, but here so is the most natural meaning.

את marks a definite direct object.

It usually appears before something specific that is receiving the action of the verb.

Here:

• אקנה את שניהם
• I will buy both of them

Even though את often has no direct English equivalent, it is an important grammatical marker in Hebrew.

שניהם means both of them for a masculine or mixed-gender pair.

Hebrew uses:

• שניהם = masculine / mixed both of them
• שתיהן = feminine both of them

Here the two things are זיתים and טחינה. Since the pair is mixed rather than fully feminine, Hebrew uses the default masculine form:

• שניהם

Because שניהם is referring to two items/categories, not matching the internal number of each noun.

In other words, the speaker is treating these as two things:

1. good olives
2. fresh tahini

So שניהם means both of those two things.

Because they are being introduced as indefinite items:

• זיתים טובים = good olives
• טחינה טרייה = fresh tahini

If the speaker meant specific known items, Hebrew might use ה־:

• הזיתים הטובים
• הטחינה הטרייה

But in an existential sentence with יש, it is very common to introduce things without ה־.

Yes. Hebrew word order is flexible, and both are natural:

• יש בחנות...
• בחנות יש...

The first version starts with the idea of there is/there are. The second version emphasizes in the store a little more.

Both are correct.