Learn Hardcore German: Sie betreibt das Café seit drei Jahren und kennt viele Gäste. - She has been running the café for three years and knows many guests.

machen is very general (to do / to make) and would sound too vague:
Sie macht das Café is not idiomatic.
führen can also mean to run / to manage (e.g. eine Firma führen), but it emphasizes leadership/management a bit more, while betreiben focuses on operating something as a business or activity.
hat (from haben) would describe possession, not activity.
Sie hat ein Café = She has/owns a café, but doesn’t necessarily say she actively runs it day to day.

So betreibt is chosen because it specifically expresses the ongoing operation of the café as a business.

Why is the present tense (betreibt) used with seit drei Jahren instead of a perfect tense like hat betrieben?

In German, when an action started in the past and is still ongoing, you normally use:

seit
- time expression
present tense

So:

Sie betreibt das Café seit drei Jahren.
= She has been running the café for three years.

In English, you need the present perfect (continuous) (has been running).
In German, the simple present is the standard choice with seit:

Ich wohne seit 2010 hier.
= I have lived / have been living here since 2010.
Er arbeitet seit einem Jahr in Berlin.
= He has worked / has been working in Berlin for a year.

Sie hat das Café seit drei Jahren betrieben would usually suggest that she ran it for three years in the past, and the period is now over. That is a different meaning.

Why is it seit drei Jahren and not seit drei Jahre? Which case is used?

After seit, German uses the dative case.

seit
- Dative

The noun das Jahr (year) declines like this:

Singular:
Nominative: das Jahr
Dative: dem Jahr
Plural:
Nominative: die Jahre
Dative: den Jahren

In seit drei Jahren, we have:

drei → plural
Jahren → dative plural form of Jahr

So the -n at the end of Jahren is the dative plural ending.

seit drei Jahre would be grammatically wrong.

What gender is Café, and why is the article das used?

Café in German is neuter, so it takes das:

das Café = the café

Many loanwords referring to places, businesses, or venues tend to be neuter:

das Restaurant
das Hotel
das Büro

The accent in Café (é) is standard in German spelling for this word and signals that the final -é is stressed: Ca-FÉ.

Why is it viele Gäste and not viel Gäste or vielen Gästen?

Three things are going on here: countable vs uncountable, plural, and case.

viel vs viele
- viel is used with uncountable nouns:
  viel Wasser (a lot of water)
  viel Geld (a lot of money)
- viele is used with countable, plural nouns:
  viele Bücher (many books)
  viele Gäste (many guests)
Since Gäste (guests) is countable and plural, we use viele, not viel.
Case of Gäste
- kennt is a transitive verb and takes a direct object in the accusative.
- wen oder was kennt sie? → viele Gäste (accusative plural)
For most nouns, nominative plural and accusative plural look the same, so Gäste stays Gäste.
Why not vielen Gästen?
- vielen Gästen would be dative plural, which is wrong here, because kennen does not take a dative object.

So viele Gäste is the correct accusative plural of viele Gäste (many guests) as the direct object of kennt.

What is the difference between kennen and wissen, and why is kennt correct here?

Both kennen and wissen translate to to know, but they are used differently:

kennen = to be familiar with someone/something
- Objects: people, places, things, works of art, etc.
- Examples:
  - Ich kenne ihn. = I know him.
  - Kennst du Berlin? = Do you know (are you familiar with) Berlin?
wissen = to know a fact / piece of information
- Objects: that-clauses, question words, facts
- Examples:
  - Ich weiß, dass er kommt. = I know that he’s coming.
  - Weißt du, wie spät es ist? = Do you know what time it is?

In the sentence:

Sie … kennt viele Gäste.

She is familiar with these people; she knows them personally. So kennen is the correct verb.

Sie weiß viele Gäste would be incorrect in German.

Could Sie here mean you (formal), or does it definitely mean she? How can I tell?

Grammatically, Sie (capital S) can mean:

she (3rd person singular)
you (formal, singular or plural)

In the form:

Sie betreibt = she runs or you (formal) run

The verb form betreibt is 3rd person singular. That fits both sie (she) and Sie (formal you).

How do we decide?

From context. The sentence as given is typically interpreted as she:
- It’s written in the 3rd person about someone who runs a café.
- If it were formal you, we would expect it in a dialogue or a direct address context.

Since the learner was given the meaning as she, we know that Sie here stands for sie = she, just capitalized at the beginning of the sentence.

Without context, the sentence on its own is ambiguous between She runs the café… and You (formal) run the café….

Is the word order fixed, or can I move seit drei Jahren to other positions in the sentence?

The word order is flexible as long as you keep main clause verb-second (V2) rule: the conjugated verb must be the second element.

Original:

Sie betreibt das Café seit drei Jahren und kennt viele Gäste.

Possible variants (all correct, slightly different emphasis):

Sie betreibt seit drei Jahren das Café und kennt viele Gäste.
– Emphasis a bit more on the time span.
Seit drei Jahren betreibt sie das Café und kennt viele Gäste.
– Strong emphasis on since three years; typical if the time information is new or important.
Das Café betreibt sie seit drei Jahren und kennt viele Gäste.
– Emphasis on das Café (contrast: not some other place).

All of these are grammatical. What must not change:

Exactly one element (a pronoun, a phrase, etc.) comes before the conjugated verb.
The conjugated verb (betreibt) remains in second position.

Why is there no comma before und in …seit drei Jahren und kennt viele Gäste?

In German, und can connect:

words
phrases
clauses

Here, und connects two main clauses that share the same subject:

Sie betreibt das Café seit drei Jahren
(sie) kennt viele Gäste

The subject Sie is only written once but applies to both verbs.

Comma rule:

If two main clauses have different, explicitly stated subjects, a comma is optional:
Sie betreibt das Café seit drei Jahren, und ihr Mann hilft ihr.
If the subject is shared and not repeated (as in this sentence), you normally do not use a comma before und, and in this specific ellipsis structure a comma is generally not allowed.

So:

Sie betreibt das Café seit drei Jahren und kennt viele Gäste. ✅
Sie betreibt das Café seit drei Jahren, und kennt viele Gäste. ❌ (incorrect in standard German)

What is the singular of Gäste, and why does the vowel change to ä in the plural?

The singular is:

der Gast = the guest

The plural is:

die Gäste = the guests

The vowel change a → ä is a common pattern in German called Umlaut. Many masculine, often monosyllabic nouns form their plural with Umlaut + -e, for example:

der Mann → die Männer (man → men)
der Wald → die Wälder (forest → forests)
der Gast → die Gäste (guest → guests)

So Gäste is just the regular plural form of Gast.